Chapter 2 Linear Equations in One Variable Ex 2.2 Solutions
Question - 11 : - Fifteen years from now Ravi’s age will be four times his present age. What is Ravi’s present age?
Answer - 11 : -
Let the present age of Ravi be x.
Fifteen years later, Ravi age will be x+15 years. According to the question,
x + 15 = 4x
⇒ 4x – x = 15
⇒ 3x = 15
⇒ x = 15/3
⇒ x = 5
Therefore, Present age of Ravi = 5 years.
Question - 12 : - The ages of Rahul and Haroon are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?
Answer - 12 : -
Let the ages of Rahul and Haroon be 5x and 7x. Four years later,
The ages of Rahul and Haroon will be (5x + 4) and (7x + 4) respectively. According to the question,
(5x + 4) + (7x + 4) = 56
⇒ 5x + 4 + 7x + 4 = 56
⇒ 12x + 8 = 56
⇒ 12x = 56 – 8
⇒ 12x = 48
⇒ x = 48/12
⇒ x = 4
Therefore, Present age of Rahul = 5x = 5×4 = 20
And, present age of Haroon = 7x = 7×4 = 28
Question - 13 : - The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8 more than the number of girls. What is the total class strength?
Answer - 13 : -
Let the number of boys be 7x and girls be 5x.
According to the question,
7x = 5x + 8
⇒ 7x – 5x = 8
⇒ 2x = 8
⇒ x = 8/2
⇒ x = 4
Therefore, Number of boys = 7×4 = 28
And, Number of girls = 5×4 = 20
Total number of students = 20+28 = 48
Question - 14 : - Baichung’s father is 26 years younger than Baichung’s grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of each one of them?
Answer - 14 : -
Let the age of Baichung’s father be x.
Then, the age of Baichung’s grandfather = (x+26)
and, Age of Baichung = (x-29) According to the question,
x + (x+26) + (x-29) = 135
⇒ 3x + 26 – 29 = 135
⇒ 3x – 3 = 135
⇒ 3x = 135 + 3
⇒ 3x = 138
⇒ x = 138/3
⇒ x = 46
Age of Baichung’s father = x = 46
Age of Baichung’s grandfather = (x+26) = 46 + 26 = 72
Age of Baichung = (x-29) = 46 – 29 = 17
Question - 15 : - A rational number is such that when you multiply it by 5/2 and add 2/3 to the product, you get -7/12. What is the number?
Answer - 15 : -
Let the rational be x.
According to the question,
x × (5/2) + 2/3 = -7/12
⇒ 5x/2 + 2/3 = -7/12
⇒ 5x/2 = -7/12 – 2/3
⇒ 5x/2 = (-7- 8)/12
⇒ 5x/2 = -15/12
⇒ 5x/2 = -5/4
⇒ x = (-5/4) × (2/5)
⇒ x = – 10/20
⇒ x = -½
Therefore, the rational number is -½.
Question - 16 : - Lakshmi is a cashier in a bank. She has currency notes of denominations ₹100, ₹50 and ₹10, respectively. The ratio of the number of these notes is 2:3:5. The total cash with Lakshmi is ₹4,00,000. How many notes of each denomination does she have?
Answer - 16 : -
Let the numbers of notes of ₹100, ₹50 and ₹10 be 2x, 3x and 5x respectively.
Value of ₹100 = 2x × 100 = 200x
Value of ₹50 = 3x × 50 = 150x
Value of ₹10 = 5x × 10 = 50x According to the question,
200x + 150x + 50x = 4,00,000
⇒ 400x = 4,00,000
⇒ x = 400000/400
⇒ x = 1000
Numbers of ₹100 notes = 2x = 2000
Numbers of ₹50 notes = 3x = 3000
Numbers of ₹10 notes = 5x = 5000