Chapter 2 Linear Equations in One Variable Ex 2.2 Solutions
Question - 1 : - The base of an isosceles triangle is 4/3 cm. The perimeter of the triangle is 
cm. What is the length of either of the remaining equal sides?
Answer - 1 : -
Base of isosceles triangle = 4/3 cm
Perimeter of triangle =
image cm = 62/15Let the length of equal sides of triangle be x.
According to the question,
4/3 + x + x = 62/15 cm
⇒ 2x = (62/15 – 4/3) cm
⇒ 2x = (62 – 20)/15 cm
⇒ 2x = 42/15 cm
⇒ x = (42/30) × (½)
⇒ x = 42/30 cm
⇒ x = 7/5 cm
The length of either of the remaining equal sides are 7/5 cm.
Question - 2 : - I have a total of ₹300 in coins of denomination ₹1, ₹2 and ₹5. The number of ₹2 coins is 3 times the number of ₹5 coins. The total number of coins is 160. How many coins of each denomination are with me?
Answer - 2 : -
Let the number of ₹5 coins be x.
Then,
number ₹2 coins = 3x
and, number of ₹1 coins = (160 – 4x) Now,
Value of ₹5 coins = x × 5 = 5x
Value of ₹2 coins = 3x × 2 = 6x
Value of ₹1 coins = (160 – 4x) × 1 = (160 – 4x)
According to the question,
5x + 6x + (160 – 4x) = 300
⇒ 11x + 160 – 4x = 300
⇒ 7x = 140
⇒ x = 140/7
⇒ x = 20
Number of ₹5 coins = x = 20
Number of ₹2 coins = 3x = 60
Number of ₹1 coins = (160 – 4x) = 160 – 80 = 80
Question - 3 : - The organisers of an essay competition decide that a winner in the competition gets a prize of ₹100 and a participant who does not win gets a prize of ₹25. The total prize money distributed is ₹3,000. Find the number of winners, if the total number of participants is 63.
Answer - 3 : -
Let the numbers of winner be x.
Then, the number of participants who didn’t win = 63 – x
Total money given to the winner = x × 100 = 100x
Total money given to participant who didn’t win = 25×(63-x)
According to the question,
100x + 25×(63-x) = 3,000
⇒ 100x + 1575 – 25x = 3,000
⇒ 75x = 3,000 – 1575
⇒ 75x = 1425
⇒ x = 1425/75
⇒ x = 19
Therefore, the numbers of winners are 19.
Question - 4 : - If you subtract 1/2 from a number and multiply the result by 1/2, you get 1/8 what is the number?
Answer - 4 : -
Let the number be x.
According to the question,
(x – 1/2) × ½ = 1/8
x/2 – ¼ = 1/8
x/2 = 1/8 + ¼
x/2 = 1/8 + 2/8
x/2 = (1+ 2)/8
x/2 = 3/8
x = (3/8) × 2
x = ¾
Question - 5 : - The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?
Answer - 5 : -
Given that,
Perimeter of rectangular swimming pool = 154 m Let the breadth of rectangle be = x
According to the question,
Length of the rectangle = 2x + 2 We know that,
Perimeter = 2(length + breadth)
⇒ 2(2x + 2 + x) = 154 m
⇒ 2(3x + 2) = 154
⇒ 3x +2 = 154/2
⇒ 3x = 77 – 2
⇒ 3x = 75
⇒ x = 75/3
⇒ x = 25 m
Therefore, Breadth = x = 25 cm
Length = 2x + 2
= (2 × 25) + 2
= 50 + 2
= 52 m
Question - 6 : - Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.
Answer - 6 : -
Let one of the numbers be= x.
Then, the other number becomes x + 15 According to the question,
x + x + 15 = 95
⇒ 2x + 15 = 95
⇒ 2x = 95 – 15
⇒ 2x = 80
⇒ x = 80/2
⇒ x = 40
First number = x = 40
And, other number = x + 15 = 40 + 15 = 55
Question - 7 : - Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers?
Answer - 7 : -
Let the two numbers be 5x and 3x. According to the question,
5x – 3x = 18
⇒ 2x = 18
⇒ x = 18/2
⇒ x = 19
Thus,
The numbers are 5x = 5 × 9 = 45
And 3x = 3 × 9 = 27.
Question - 8 : - Three consecutive integers add up to 51. What are these integers?
Answer - 8 : -
Let the three consecutive integers be x, x+1 and x+2. According to the question,
x + (x+1) + (x+2) = 51
⇒ 3x + 3 = 51
⇒ 3x = 51 – 3
⇒ 3x = 48
⇒ x = 48/3
⇒ x = 16
Thus, the integers are
x = 16
x + 1 = 17
x + 2 = 18
Question - 9 : - The sum of three consecutive multiples of 8 is 888. Find the multiples.
Answer - 9 : -
Let the three consecutive multiples of 8 be 8x, 8(x+1) and 8(x+2). According to the question,
8x + 8(x+1) + 8(x+2) = 888
⇒ 8 (x + x+1 + x+2) = 888 (Taking 8 as common)
⇒ 8 (3x + 3) = 888
⇒ 3x + 3 = 888/8
⇒ 3x + 3 = 111
⇒ 3x = 111 – 3
⇒ 3x = 108
⇒ x = 108/3
⇒ x = 36
Thus, the three consecutive multiples of 8 are:
8x = 8 × 36 = 288
8(x + 1) = 8 × (36 + 1) = 8 × 37 = 296
8(x + 2) = 8 × (36 + 2) = 8 × 38 = 304
Question - 10 : - Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.
Answer - 10 : -
Let the three consecutive integers are x, x+1 and x+2. According to the question,
2x + 3(x+1) + 4(x+2) = 74
⇒ 2x + 3x +3 + 4x + 8 = 74
⇒ 9x + 11 = 74
⇒ 9x = 74 – 11
⇒ 9x = 63
⇒ x = 63/9
⇒ x = 7
Thus, the numbers are:
x = 7
x + 1 = 8
x + 2 = 9