Chapter 2 Linear Equations in One Variable Exercise 2.2
Question 1: If you subtract 1/2 from a number and multiply the result by 1/2, you will get 1/8. What is the number?Answer:
Let the three consecutive integers be x, x + 1 and x + 2.
= 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
x = 7
x + 1 = 7 + 1 = 8
x + 2 = 7 + 2 = 9
Question 9: The age of Rahul and Haroon are in the ratio 5:7. Four years later sum of their ages will be 56 years. What are their present ages?

Present Age 
Age after 4 years 
Rahul 
5x 
5x + 4 
Haroon 
7x 
7x + 4 
= 5x + 4 + 7x + 4 = 56
= 12x + 8 = 56
= 12x = 56  8
= 12x = 48
= x = 48/12
= x = 4
= 5x = 5 × 4 = 20
= 7x = 7 × 4 = 28
Therefore, the age of Rahul is 20 years while the age of Haroon is 28 years.
Question 10: 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:
Let the number of boys and girls be 7x and 5x.
= 7x = 5x + 8
= 7x  5x = 8
= 2x = 8
= x = 8/2
= x = 4
7x = 7 × 4 = 28
5x = 5 × 4 = 20
= Total strength = Number of Boys + Number of Girls
= 28 + 20
= 48
Therefore, 48 is the total class strength.
Question 11: 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:
Baichung age = x years
Baichung's father age = x + 29 years
Baichung's grandfather age = x + 29 + 26 years
= x + x + 29 + x + 29 + 26 = 135
= 3x + 84 = 135
= 3x = 135  84
= 3x = 51
= x = 51/3
= x = 17
Age
Baichung = x = 17 years
Baichung's father age = 17 + 29 = 46 years
Baichung's grandfather age = 17 + 29 + 26 = 72 years
Question 12: Fifteen years from now Ravi’s age will be four times his present age. What is Ravi’s present age?
Answer:

Present Age 
Age after 15 years 
Ravi 
x 
x + 15 
= x + 15 = 4x
= 15 = 4x  x
= 15 = 3x
= 15/3 = x
= 5 = x
= x = 5
Therefore, Ravi's present age is 5 years.
Question 13: 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:
Let the rational number be x.
Given
5x/2 + 2/3 = 7/12
= 5x/2 = 712  2/3
= 5x/2 = 15/12
= x = 15/12 × 2/5
= x = 30/60
= x = 1/2
Therefore, the rational number is 1/2.
Question 14: 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:
Denomination 
Number 
Amount 
₹100 
2x 
200x 
₹50 
3x 
150x 
₹10 
5x 
50x 
= 200x + 150x + 50x = 400000
= 400x = 400000
= x = 400000/400
= x = 1000
Denomination 
Number 
Amount 
₹100 
2x (2000 notes) 
200x (₹200000) 
₹50 
3x (3000 notes) 
150x (₹150000) 
₹10 
5x (5000 notes) 
50x (₹50000) 
Therefore, she has 2000 notes of ₹100, 3000 notes of ₹50 and 5000 notes of ₹10.
Question 15: 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:
Denomination 
Number 
Amount 
₹1 
160  4x 
160  4x 
₹2 
3x 
6x 
₹5 
x 
5x 

160 
₹300 
= 160  4x + 6x + 5x = 300
= 160 + 7x = 300
= 7x = 300  160
= 7x = 140
= x = 140/7
= x = 20
Denomination 
Number 
Amount 
₹1 
160  4x (80 coins) 
160  4x (₹80) 
₹2 
3x (60 coins) 
6x (₹120) 
₹5 
x (20 coins) 
5x (₹100) 

160 
₹300 
Therefore, I have 80 coins of ₹1, 60 coins of ₹2 and 20 coins of ₹5.
Question 16: 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:
Let the numbers of winner be x.
The number of participants who didn’t win will be 63  x.
Amount given to the winner = ₹(100 × x) = ₹100x
Amount given to participant who didn’t win = ₹25(63  x)
= ₹(1575  25x)
= 100x + 1575  25x = 3000
= 75x = 3000  1575
= 75x = 1425
= x = 1425/75
= x = 19
Therefore, the numbers of winners are 19.
No comments:
Post a Comment