Math Ncert Exemplar 2019 Solutions for Class 8 Maths Chapter 4 Linear Equation In One Variable are provided here with simple step-by-step explanations. These solutions for Linear Equation In One Variable are extremely popular among class 8 students for Maths Linear Equation In One Variable Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Math Ncert Exemplar 2019 Book of class 8 Maths Chapter 4 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Math Ncert Exemplar 2019 Solutions. All Math Ncert Exemplar 2019 Solutions for class 8 Maths are prepared by experts and are 100% accurate.
Page No 110:
Question 1:
In questions âout of the four options only one is correct.
The solution of which of the following equations is neither a fraction nor an integer.
(a) 3x + 2 = 5x + 2
(b) 4x – 18 = 2
(c) 4x + 7 = x + 2
(d) 5x – 8 = x + 4
Answer:
Case I: 3x + 2 = 5x + 2
⇒ 2 – 2 = 5x – 3x [transposing 3x to LHS and 2 to RHS]
[dividing both ides by 2]
⇒ x = 0
Thus, it's an integer.
Case II: 4x – 18 = 2
⇒ 4x = 2 + 18 [transposing –18 to RHS]
[dividing both ides by 2]
Thus, it's an integer
Case III: 4x + 7 = x + 2
⇒ 4x – x = 2 – 7 [transposing x to LHS and 7 to RHS]
[dividing both ides by 2]
Thus, it's neither a fraction nor an integer
Case IV: 5x – 8 = x + 4
⇒ 5x – x = 8 + 4 [transposing x to LHS and –8 to RHS]
[dividing both ides by 4]
Thus, it is an integer.
Hence, the correct answer is option C.
Page No 110:
Question 2:
In questions âout of the four options only one is correct.
The solution of the equation ax + b = 0 is
(a)
(b)
(c)
(d)
Answer:
Given: ax + b = 0
[transposing b to RHS]
[dividing both sides by a]
Hence, the correct answer is option C.
Page No 111:
Question 3:
In questions âout of the four options only one is correct.
If 8x – 3 = 25 + 17x, then x is
(a) a fraction
(b) an integer
(c) a rational number
(d) cannot be solved
Answer:
Given: 8x – 3 = 25 + 17x
⇒ 8x – 17x = 25 + 3 [transposing 17x on LHS and –3 on RHS]
[dividing both sides by –9]
Thus, it is a rational number
Hence, the correct answer is option C.
Page No 111:
Question 4:
In questions âout of the four options only one is correct.
The shifting of a number from one side of an equation to other is called
(a) Transposition
(b) Distributivity
(c) Commutativity
(d) Associativity
Answer:
The shifting of a number from one side of an equation to other side is called transposition.
Say for example: x + 7 = 0 is the equation ⇒ x = –7 Here, the number ‘7’ shifts from left hand side to right hand side.
Hence, the correct answer is option A.
Page No 111:
Question 5:
In questions âout of the four options only one is correct.
If , then the numerical value of 2x – 7 is
(a)
(b)
(c) 0
(d)
Answer:
Given:
[transposing on LHS and –4 on RHS]
[simplification of equation]
[dividing both sides by 19]
To find value of 2x – 7, putting the value from (1)
[simplification of equation]
Thus the value of 2x –7, when is
Hence, the correct answer is option B.
Page No 111:
Question 6:
In questions âout of the four options only one is correct.
The value of x for which the expressions 3x – 4 and 2x + 1 become equal is
(a) –3
(b) 0
(c) 5
(d) 1
Answer:
Given: 3x – 4 = 2x + 1
⇒ 3x – 2x = 4 + 1 [transposing 2x on LHS and –4 on RHS]
⇒ x = 5
Thus, for x = 5 the expressions 2x – 4 and 2x + 1 becomes equal.
Hence, the correct answer is option C.
Page No 111:
Question 7:
In questions âout of the four options only one is correct.
If a and b are positive integers, then the solution of the equation ax = b has to be always
(a) positive
(b) negative
(c) one
(d) zero
Answer:
Given: ax = b
[dividing both sides by a]
As, a and b both are positive thus the solution of ax = b will always be positive.
Hence, the correct answer is option A.
Page No 111:
Question 8:
In questions âout of the four options only one is correct.
Linear equation in one variable has
(a) only one variable with any power.
(b) only one term with a variable.
(c) only one variable with power 1.
(d) only constant term.
Answer:
Only one variable of power 1 exists in a linear equation in one variable. For example: 5x – 1 = 2, 2p – 9 = 3 and z + 20 = – 8 are the linear equations in one variable.
Hence, the correct answer is option C.
Page No 112:
Question 9:
In questions âout of the four options only one is correct.
Which of the following is a linear expression:
(a) x2 + 1
(b) y + y2
(c) 4
(d) 1 + z
Answer:
The linear expression is defined as an algebraic expression in one variable with the maximum power of the variable equal to 1.
Because the power of the variable z is 1, the only linear expression is 1 + z.
Hence, the correct answer is option D.
Page No 112:
Question 10:
In questions âout of the four options only one is correct.
A linear equation in one variable has
(a) Only one solution
(b) Two solutions
(c) More than two solutions
(d) No solution
Answer:
There is only one solution to a linear equation with one variable.
For Example: the linear equation ax + b = 0 has unique solution.
Hence, the correct answer is option A.
Page No 112:
Question 11:
In questions âout of the four options only one is correct.
Value of S in S =
(a)
(b)
(c) 10
(d) 0
Answer:
Given:
[transposing to RHS]
[taking LCM in RHS]
Hence, the correct answer is option B.
Page No 112:
Question 12:
In questions âout of the four options only one is correct.
, then y =
(a)
(b)
(c)
(d)
Answer:
Given:
[By cross multiplication]
Thus, the value of y is
Hence, the correct answer is option C.
Page No 112:
Question 13:
In questions âout of the four options only one is correct.
The digit in the tens place of a two digit number is 3 more than the digit in the units place. Let the digit at units place be b. Then the number is
(a) 11b + 30
(b) 10b + 30
(c) 11b + 3
(d) 10b + 3
Answer:
The digit at unit’s place is b.
Then, digit at ten’s place = (3 + b)
Therefore, the number = 10 (3 + b) + b
= 30 + 10b + b
= 11b + 30
Hence, the correct answer is option A.
Page No 112:
Question 14:
In questions âout of the four options only one is correct.
Arpita’s present age is thrice of Shilpa. If Shilpa’s age three years ago was x. Then Arpita’s present age is
(a) 3(x – 3)
(b) 3x + 3
(c) 3x – 9
(d) 3(x + 3)
Answer:
Given, Shilpa’s age three years ago = x
Then, Shilpa’s present age = (x + 3)
Arpita’s present age = 3 x Shilpa’s present age = 3 (x + 3)
Hence, the correct answer is option D.
Page No 113:
Question 15:
In questions âout of the four options only one is correct.
The sum of three consecutive multiples of 7 is 357. Find the smallest multiple.
(a) 112
(b) 126
(c) 119
(d) 116
Answer:
Let the 3 consecutive multiple of 7 be 7x, (7x + 7) and (7x + 14), where x is a natural number
Then, 7x + 7x + 7 + 7x + 14 = 357
⇒ 21x + 21 = 357
⇒ 21(x + 1) = 357
⇒ [dividing both sides by 21]
⇒ x + 1 = 17
⇒ x = 17 – 1 [transposing 1 to RHS]
∴ x = 16
Thus, the smallest multiplying of 7 is 7 × 16 = 112
Hence, the correct answer is option A.
Page No 113:
Question 16:
In questions âfill in the blanks to make each statement true.
In a linear equation, the _________ power of the variable appearing in the equation is one.
Answer:
highest
Page No 113:
Question 17:
In questions âfill in the blanks to make each statement true.
The solution of the equation 3x – 4 = 1 – 2 x is _________.
Answer:
3x – 4 = 1 – 2 x
⇒ 3x + 2x = 1 + 4 [transposing like terms together]
⇒ 5x = 5 [dividing both sides by 5]
⇒
⇒ x = 1
∴ solution of equation is x = 1.
Page No 113:
Question 18:
In questions âfill in the blanks to make each statement true.
The solution of the equation 2y = 5y – is _________.
Answer:
Given, 2y = 5y –
[transposing like terms together]
[dividing both side by 3]
∴ solution of equation ⇒
Page No 113:
Question 19:
In questions âfill in the blanks to make each statement true.
Any value of the variable which makes both sides of an equation equal is known as a _________ of the equation.
Answer:
solution
Page No 113:
Question 20:
In questions âfill in the blanks to make each statement true.
9x – _________ = –21 has the solution (–2)
Answer:
9x – _______ = –21 ...(1)
where the solution of equation is x = –2.
Putting x = –2 in (1),
9(–2) −_______ = –21
⇒ –18 – ________ = –21
⇒ –18 + 21 = ________ (Transposing)
⇒ 3 = ________
∴ ans = 3.
Page No 113:
Question 21:
In questions âfill in the blanks to make each statement true.
Three consecutive numbers whose sum is 12 are _________, _________ and _________.
Answer:
3, 4, 5
as (3 + 4) + 5 = 7 + 5
Page No 113:
Question 22:
In questions âfill in the blanks to make each statement true.
The share of A when Rs 25 are divided between A and B so that A gets Rs. 8 more than B is _________.
Answer:
A gets â¹8 more than B.
Let us suppose that B has â¹b.
⇒ A has = â¹(b + 8)
Now, the sum of the amounts of money they have = â¹25
⇒ money with A + money with B = â¹25
⇒ â¹(b + 8) + â¹b = â¹25
⇒â¹b + â¹8 + â¹b = â¹25
⇒ â¹2b + â¹8 = 25
⇒ â¹2b = 25 – 8
b = â¹8.5
Page No 113:
Question 23:
In questions âfill in the blanks to make each statement true.
A term of an equation can be transposed to the other side by changing its _________.
Answer:
sign
Page No 113:
Question 24:
In questions âfill in the blanks to make each statement true.
On subtracting 8 from x, the result is 2. The value of x is _________.
Answer:
x – 8 = 2
⇒ x = 2 + 8 (Transposing like terms together)
Page No 113:
Question 25:
In questions âfill in the blanks to make each statement true.
has the solution as _________.
Answer:
cross multiplying,
⇒ x × 1 = –12 × 5
⇒ x = –60.
∴ solution of equation ⇒ x = –60.
Page No 113:
Question 26:
In questions âfill in the blanks to make each statement true.
When a number is divided by 8, the result is –3. The number is _________.
Answer:
Let the number be x
cross multiplying, we get
⇒ x × 1 = –3 × 8
⇒ x = –24
Hence, the number is –24.
Page No 113:
Question 27:
In questions âfill in the blanks to make each statement true.
9 is subtracted from the product of p and 4, the result is 11. The value of p is _________.
Answer:
Given, 4p – 9 = 11
Hence, the value of p is 5.
Page No 113:
Question 28:
In questions âfill in the blanks to make each statement true.
If , then x = _________.
Answer:
Given,
Page No 113:
Question 29:
In questions âfill in the blanks to make each statement true.
After 18 years, Swarnim will be 4 times as old as he is now. His present age is _________.
Answer:
Let the present age be x.
Age after 18 years = x + 18
Given,
Hence, present age is 6 years.
Page No 113:
Question 30:
In questions âfill in the blanks to make each statement true.
Convert the statement Adding 15 to 4 times x is 39 into an equation _________.
Answer:
Given, add 15 to 4x which equals 39
⇒ 4x + 15 = 39
Hence, the equation is 4x + 15 = 39.
Page No 115:
Question 31:
In questions âfill in the blanks to make each statement true.
The denominator of a rational number is greater than the numerator by 10. If the numerator is increased by 1 the and denominator is decreased by 1, then expression for new denominator is _________.
Answer:
Page No 115:
Question 32:
In questions âfill in the blanks to make each statement true.
The sum of two consecutive multiples of 10 is 210. The smaller multiple is _________.
Answer:
Let the consecutive multiple be x and x + 10.
Given,
The smaller multiple is 100.
Page No 115:
Question 33:
State whether the statements are true (T) or false (F).
3 years ago, the age of a boy was y years. His age 2 years ago was (y – 2) years.
Answer:
Statement is False
Given, 3 year ago, age of boy = y
Then, present age of boy = (y + 3)
Hence, 2 year ago age of boy = y + 3 – 2 = y + 1
Page No 115:
Question 34:
State whether the statements are true (T) or false (F).
Shikha’s present age is p years. Reemu’s present age is 4 times the present age of Shikha. After 5 years Reemu’s age will be 15p years.
Answer:
Statement is False
Given, Shikha’s present age = p year
Then, Reemu’s present age = 4x (Shikha’s present age) = 4p year
Therefore after 5 year, Reemu’s age is = (4p + 5) year
Page No 115:
Question 35:
State whether the statements are true (T) or false (F).
In a 2 digit number, the units place digit is x. If the sum of digits be 9, then the number is (10x – 9).
Answer:
The statement is False
Given, unit’s digit = x
and sum of digits = 9
Ten’s digit = 9 – x
Hence, the number = 10 (9 – x) + x
= 90 – 10x + x
= 90 – 9x
Page No 115:
Question 36:
State whether the statements are true (T) or false (F).
Sum of the ages of Anju and her mother is 65 years. If Anju’s present age is y years then her mother’s age before 5 years is (60 – y) years.
Answer:
The statement is True
Given, Anju’s present age = y year
Then, Anju’s mother age = (65 – y) year
5-year before, Anju’s mother age = 65 – y – 5
= (60 – y) year
Page No 115:
Question 37:
State whether the statements are true (T) or false (F).
The number of boys and girls in a class are in the ratio 5:4. If the number of boys is 9 more than the number of girls, then number of boys is 9.
Answer:
The statement is False
Let the number of boys be 5x and the number of girls be 4x.
According to the question, 5x = 4x + 9
5x – 4x = 9 [Transposing 4x to LHS]
x = 9
Hence, number of boys = 5 × 9 = 45
Page No 115:
Question 38:
State whether the statements are true (T) or false (F).
A and B are together 90 years old. Five years ago A was thrice as old as B was. Hence, the ages of A and B five years back would be (x – 5) years and (85 – x) years respectively.
Answer:
The statement is True
Let the age of A be x year
Then, age of B = (90 – x) year
Five years ago, the age of A = (x – 5) year
The age of B = 90 – x – 5 = (85 – x) year
Hence, the ages of A and B five years back would be (x – 5) year and (85 – x) year.
Page No 115:
Question 39:
State whether the statements are true (T) or false (F).
Two different equations can never have the same answer.
Answer:
The statement is False
Two different equations may have the same answer.
e.g. 3x + 6 = 9 and 4x – 3 = 1 are the two linear equations whose solution is 1.
Page No 115:
Question 40:
State whether the statements are true (T) or false (F).
In the equation 3x – 3 = 9, transposing –3 to RHS, we get 3x = 9.
Answer:
The statement is False
Given, 3x – 3 = 9
3x = 9 + 3 [transposing –3 to RHS]
3x = 12
Page No 115:
Question 41:
State whether the statements are true (T) or false (F).
In the equation 2x = 4 – x, transposing –x to LHS, we get x = 4.
Answer:
The statement is False
Given, 2x = 4 – x
⇒ 2x + x = 4 [transposing – x to LHS]
⇒ 3x = 4
Page No 115:
Question 42:
State whether the statements are true (T) or false (F).
If
Answer:
The statement is False
Page No 115:
Question 43:
State whether the statements are true (T) or false (F).
If
Answer:
The statement is False
Given,
Page No 115:
Question 44:
State whether the statements are true (T) or false (F).
If 6x = 18, then 18x = 54
Answer:
The statement is True
Given, 6x = 18
Page No 115:
Question 45:
State whether the statements are true (T) or false (F).
If
Answer:
The statement is False
Given,
Page No 115:
Question 46:
State whether the statements are true (T) or false (F).
If x is an even number, then the next even number is 2(x + 1).
Answer:
The statement is False
Given, x is an even number.
Then, the next even number is (x + 2).
Page No 116:
Question 47:
State whether the statements are true (T) or false (F).
If the sum of two consecutive numbers is 93 and one of them is x, then the other number is 93 – x.
Answer:
The statement is True
Given, one of the consecutive number is = x
Then, the next consecutive number = x + 1
So,
Hence, the other consecutive number = 46 + 1 = 47
⇒ 93 – 46 = 93 – x
Page No 116:
Question 48:
State whether the statements are true (T) or false (F).
Two numbers differ by 40, when each number is increased by 8, the bigger becomes thrice the lesser number. If one number is x, then the other number is (40 – x).
Answer:
The statement is False.
Given, one number = x
other number = 40 – x
Let (40 – x) > x
So,
Hence, one number is 6.
other number is = 40 – 6 = 34
The difference between the numbers = 34 – 6 = 28 ≠ 40.
Page No 116:
Question 49:
Solve the following:
Answer:
Given,
Page No 116:
Question 50:
Solve the following:
Answer:
Given,
Page No 116:
Question 51:
Solve the following:
Answer:
Given,
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Question 52:
Solve the following:
Answer:
Given,
Page No 116:
Question 53:
Solve the following:
Answer:
Given,
Page No 116:
Question 54:
Solve the following:
Answer:
Given,
Page No 116:
Question 55:
Solve the following:
Answer:
Given,
Page No 116:
Question 56:
Solve the following:
Answer:
Given,
Page No 116:
Question 57:
Solve the following:
0.4(3x –1) = 0.5x + 1
Answer:
Given, 0.4(3x –1) = 0.5x + 1
Page No 116:
Question 58:
Solve the following:
8x – 7 – 3x = 6x – 2x – 3
Answer:
Page No 116:
Question 59:
Solve the following:
10x – 5 – 7x = 5x + 15 – 8
Answer:
Given, 10x – 5 – 7x = 5x + 15 – 8
Page No 116:
Question 60:
Solve the following:
4t – 3 – (3t +1) = 5t – 4
Answer:
Given, 4t – 3 – (3t +1) = 5t – 4
Page No 116:
Question 61:
Solve the following:
5(x – 1) – 2(x + 8) = 0
Answer:
Given, 5(x – 1) – 2(x + 8) = 0
Page No 116:
Question 62:
Solve the following:
Answer:
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Question 63:
Solve the following:
Answer:
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Question 64:
Solve the following:.
Answer:
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Question 65:
Solve the following:.
Answer:
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Question 66:
Solve the following:.
Answer:
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Question 67:
Solve the following:.
Answer:
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Question 68:
Solve the following:.
Answer:
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Question 69:
Solve the following:.
Answer:
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Question 70:
Solve the following:.
Answer:
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Question 71:
Solve the following:.
Answer:
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Question 72:
Solve the following:.
Answer:
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Question 73:
Solve the following:.
Answer:
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Question 74:
Solve the following:.
Answer:
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Question 75:
Solve the following:.
Answer:
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Question 76:
Solve the following:.
4 (3p + 2) – 5(6p –1) = 2(p – 8) – 6(7p – 4)
Answer:
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Question 77:
Solve the following:.
3(5x – 7) + 2(9x – 11) = 4(8x – 7) – 111
Answer:
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Question 78:
Solve the following:.
0.16(5x – 2) = 0.4x + 7
Answer:
Page No 117:
Question 79:
Radha takes some flowers in a basket and visits three temples one by one. At each temple, she offers one half of the flowers from the basket.
If she is left with 3 flowers at the end, find the number of flowers she had in the beginning.
Answer:
Let the number of flowers be x.
The number of flowers offered in first temple =
The number of flowers offered in second temple =
The number of flowers offered in third temple =
According to the question,
Hence, total number of flowers in the beginning were 24.
Page No 118:
Question 80:
â¹13500 are to be distributed among Salma, Kiran and Jenifer in such a way that Salma gets â¹1000 more than Kiran and Jenifer gets â¹500 more than Kiran. Find the money received by Jenifer.
Answer:
Let the money received by Kiran be x.
Then, the money received by Salma = x + 1000
And, the money received by Jenifer = x + 500
According to the question,
x + x + 500 + x + 1000 = 13500
So, money received by Jenifer is â¹4500.
Page No 118:
Question 81:
The volume of water in a tank is twice of that in the other. If we draw out 25 litres from the first and add it to the other, the volumes of the water in each tank will be the same. Find the volume of water in each tank.
Answer:
Let the volume of the water in second tank be x.
Then, the volume of the water in first tank will be 2x.
According to the question,
Hence, volume of water in one tank is 50 L and in the other tank is 100 L.
Page No 118:
Question 82:
Anushka and Aarushi are friends. They have equal amount of money in their pockets. Anushka gave of her money to Aarushi as her birthday gift. Then Aarushi gave a party at a restaurant and cleared the bill by paying half of the total money with her. If the remaining money in Aarushi’s pocket is Rs.1600, find the sum gifted by Anushka.
Answer:
Let Anushka and Arushi have equal amount of money in their pocket i.e. x.
After giving of Anushka's money to Arushi, the amount with Arushi = .
According to the question,
Hence, money gifted by Anushka is â¹800.
Page No 118:
Question 83:
Kaustubh had 60 flowers. He offered some flowers in a temple and found that the ratio of the number of remaining flowers to that of flowers in the beginning is 3:5. Find the number of flowers offered by him in the temple.
Answer:
Let the number of flowers offered by Kaustubh in the temple be x.
Then, the flowers remaining = 60 − x
According to the question,
Hence, the number of flowers offered by him in the temple is 24.
Page No 118:
Question 84:
The sum of three consecutive even natural numbers is 48. Find the greatest of these numbers.
Answer:
Let the three consecutive even natural numbers be x, x + 2, x + 4.
According to the question,
Therefore, the three consecutive even natural numbers are 14, 16, 18.
Hence, the greatest of the three consecutive numbers is 18.
Page No 118:
Question 85:
The sum of three consecutive odd natural numbers is 69. Find the prime number out of these numbers.
Answer:
Let the three consecutive odd natural numbers be x, x + 2, x + 4.
According to the question,
The three consecutive odd natural numbers are 21, 23, 25.
Hence, the prime number is 23.
Page No 118:
Question 86:
The sum of three consecutive numbers is 156. Find the number which is a multiple of 13 out of these numbers.
Answer:
Let the three consecutive natural numbers be x, x + 1, x + 2.
According to the question,
The three consecutive natural numbers are 51, 52, 53.
Hence, the multiple of 13 is 52.
Page No 118:
Question 87:
Find a number whose fifth part increased by 30 is equal to its fourth part decreased by 30.
Answer:
Let the number be x.
According to the question,
Hence, the required number is 1200.
Page No 118:
Question 88:
Divide 54 into two parts such that one part is of the other.
Answer:
Let the other part be x. Then, the first part will be .
According to the question,
Hence, the two parts are 12 and 42.
Page No 118:
Question 89:
Sum of the digits of a two-digit number is 11. The given number is less than the number obtained by interchanging the digits by 9. Find the number.
Answer:
Let the units digit be x. Then, the tens digit will be 11 − x.
So, the number will be = 110 − 9x.
By interchanging the digits, we get = 9x + 11.
According to the question,
So, units digit is 6 and tens digit is 5.
Hence, the number so formed is 56.
Page No 118:
Question 90:
Two equal sides of a triangle are each 4m less than three times the third side. Find the dimensions of the triangle, if its perimeter is 55 m.
Answer:
Let the third side be x.
Then, the two other sides = 3x − 4.
Perimeter of the triangle = 55
Hence, the dimensions of the triangle are 9 m, 23 m and 23 m.
Page No 119:
Question 91:
After 12 years, Kanwar shall be 3 times as old as he was 4 years ago. Find his present age.
Answer:
Let Kanwar's present age be x years.
After 12 years, Kanwar's age = (x + 12) years
And, four years ago, Kanwar's age = (x − 4) years
According to the question,
Hence, the present age is 12 years.
Page No 119:
Question 92:
Anima left one-half of her property to her daughter, one-third to her son and donated the rest to an educational institute. If the donation was worth Rs. 1,00,000, how much money did Anima have?
Answer:
Let Anima's property be x.
Property left for daughter =
Remaining property =
Property remaining for the son =
Remaining property =
Now,
Remaining property = donation money
Hence, Anima had â¹300000.
Page No 119:
Question 93:
If is subtracted from a number and the difference is multiplied by 4, the result is 5. What is the number?
Answer:
Let the number be x.
According to the question,
Hence, the required number is .
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Question 94:
The sum of four consecutive integers is 266. What are the integers?
Answer:
Let the four consecutive integers be x, x + 1, x + 2, x + 3.
According to the question,
Hence, the four consecutive integers are 65, 66, 67 and 68.
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Question 95:
Hamid has three boxes of different fruits. Box A weighs kg more than Box B and Box C weighs kg more than Box B. The total weight of the three boxes is kg. How many kilograms (kg) does Box A weigh?
Answer:
Let the weight of box A be x kg.
Then, weight of box B = kg
And, weight of box C = kg
According to the question,
Hence, box A weighs kg.
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Question 96:
The perimeter of a rectangle is 240 cm. If its length is increased by 10% and its breadth is decreased by 20%, we get the same perimeter. Find the length and breadth of the rectangle.
Answer:
Perimeter of rectangle = 240
⇒ 2(Length + Breadth) = 240
⇒ Length + Breadth = 120
Let the length of the rectangle be x.
⇒ Breadth = 120 − x
New length of rectangle =
New breadth of rectangle =
According to the question,
Hence, length is 80 cm and breadth is 40 cm.
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Question 97:
The age of A is five years more than that of B. 5 years ago, the ratio of their ages was 3 : 2. Find their present ages.
Answer:
Let the present age of B be years.
Then, the present age of A will be years.
Five years ago,
age of A = years
age of B = years
According to the question,
Hence, the present age of B is 15 years and that of A is 20 years.
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Question 98:
If numerator is 2 less than denominator of a rational number and when 1 is subtracted from numerator and denominator both, the rational number in its simplest form is . What is the rational number?
Answer:
Let the denominator be x.
Then, the numerator =
According to the question,
Hence, the denominator is 5, numerator is 3 and the rational number is .
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Question 99:
In a two digit number, digit in units place is twice the digit in tens place. If 27 is added to it, digits are reversed. Find the number.
Answer:
Let the tens digit of a two digit number be x.
Then, units digit will be 2x.
So, the number will be 10x + 2x = 12x.
On reversing the digits, the new number will be .
According to the question,
Hence, the required number is 36.
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Question 100:
A man was engaged as typist for the month of February in 2009. He was paid Rs. 500 per day but Rs. 100 per day were deducted for the days he remained absent. He received Rs. 9,100 as salary for the month. For how many days did he work?
Answer:
Let the number of days the man worked in February 2009 be x.
Then, number of days the man was absent in the month of February = 29 − x.
So, total amount paid for working days in February = â¹500x
And, total amount deducted for being absent = â¹100 × (29 − x)
According to the question,
Therefore, the man worked for 20 days.
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Question 101:
A steamer goes downstream and covers the distance between two ports in 3 hours. It covers the same distance in 5 hours when it goes upstream. If the stream flows at 3 km/hr, then find what is the speed of the steamer upstream?
Answer:
Let the speed of the streamer in still water be x km/h.
Speed of the stream = 3 km/h
Speed of the streamer downstream = (x + 3) km/h
Speed of the streamer upstream = (x − 3) km/h
According to the question,
Hence, the speed of the streamer upstream is 9 km/h.
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Question 102:
A lady went to a bank with Rs. 1,00,000. She asked the cashier to give her Rs. 500 and Rs. 1,000 currency notes in return. She got 175 currency notes in all. Find the number of each kind of currency notes.
Answer:
Let the total number of notes of â¹500 be x.
Then, total number of notes of â¹1000 = 175 − x
According to the question,
Hence, total number of notes of â¹500 is 150 and notes of â¹1000 is 25.
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Question 103:
There are 40 passengers in a bus, some with Rs. 3 tickets and remaining with Rs.10 tickets. The total collection from these passengers is Rs. 295. Find how many passengers have tickets worth Rs. 3?
Answer:
Let the number of passengers having tickets worth â¹3 be x.
Then, the number of passengers having tickets worth â¹10 will be (40 − x).
According to the question,
Hence, the number of passengers having tickets worth â¹3 is 15.
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Question 104:
Denominator of a number is 4 less than its numerator. If 6 is added to the numerator it becomes thrice the denominator. Find the fraction.
Answer:
Let the numerator be x.
Then, the denominator will be x − 4.
According to the question,
Hence, the fraction is .
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Question 105:
An employee works in a company on a contract of 30 days on the condition that he will receive Rs. 120 for each day he works and he will be fined Rs. 10 for each day he is absent. If he receives Rs. 2300 in all, for how many days did he remain absent?
Answer:
Let the number of days the employee was absent be x.
Then, the number of days the employee worked = (30 − x)
According to the question,
Hence, the employee remained absent for 10 days.
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Question 106:
Kusum buys some chocolates at the rate of Rs. 10 per chocolate. She also buys an equal number of candies at the rate of Rs. 5 per candy. She makes a 20% profit on chocolates and 8% profit on candies. At the end of the day, all chocolates and candies are sold out and her profit is Rs. 240. Find the number of chocolates purchased.
Answer:
Let the number of chocolates Kusum purchased be x.
Then, total cost of chocolates = â¹10x
Let the number of candies Kusum purchased be x.
Then, total cost of chocolates = â¹5x
According to the question,
Total profit = 2.4x
Hence, Kusum purchased 100 chocolates.
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Question 107:
A steamer goes downstream and covers the distance between two ports in 5 hours while it covers the same distance upstream in 6 hours. If the speed of the stream is 1 km/hr, find the speed of the steamer in still water.
Answer:
Let the speed of the streamer in still water be x.
Then, speed of the streamer downstream = (x + 1) km/h
And, speed of the streamer upstream = (x − 1) km/h
According to the question,
Hence, speed of the streamer in still water is 11 km/h.
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Question 108:
Distance between two places A and B is 210 km. Two cars start simultaneously from A and B in opposite direction and distance between them after 3 hours is 54 km. If speed of one car is less than that of other by 8 km/hr, find the speed of each.
Answer:
Let the speed of the car starting from A be x km/h.
Then, speed of the car starting from B = (x + 8) km/h
According to the question,
Hence, speed of car starting from A is 22 km/h and from B is 30 km/h.
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Question 109:
A carpenter charged Rs. 2500 for making a bed. The cost of materials used is Rs. 1100 and the labour charges are Rs. 200/hr. For how many hours did the carpenter work?
Answer:
Let the carpenter work for x hours.
Then, total labour charges = 200x
According to the question,
Amount charged by the carpenter = Labour charges + Cost of material
Hence, the carpenter worked for 7 hours.
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Question 110:
For what value of x is the perimeter of shape 77 cm?
Answer:
Perimeter of the shape = Sum of all its sides
Hence, the value of x is 10 cm.
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Question 111:
For what value of x is the perimeter of shape 186 cm?
Answer:
Perimeter of a rectangle = 2(Length + Breadth)
Hence, the value of x is 3 cm.
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Question 112:
On dividing Rs. 200 between A and B such that twice of A’s share is less than 3 times B’s share by 200, B’s share is?
Answer:
Let B's share be x.
Then, A's share = 200 − x
According to the question,
Hence, B's share is â¹120.
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Question 113:
Madhulika thought of a number, doubled it and added 20 to it. On dividing the resulting number by 25, she gets 4. What is the number?
Answer:
Let the number be x.
According to the question,
Hence, the required number is 40.
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