NCERT Math Solutions for CBSE Class 8
Class 8 Mathematics Solutions of NCERT Maths Exercise 2.2
Linear Equations in One Variable
(page
28)
View solutions for Question No.1 - 8
Q 9: The ages for Rahul
and Haroon are in the ration of 5 : 7. Four years later the sum of their ages
will be 56 years. What are their present ages?
Solution:
Let the ratios are in x
Then Rahul’s present age = 5x years
Haroon’s present age = 7x years
Four years later Rahul’s age will be =
(5x + 4) years
Four years later Haroon’s age will be =
(7x + 4) years
As per the given condition,
5x
+ 4 + 7x + 4 = 56
or, x
= 4
Putting the value of x above we get,
Rahul’s present age = 5 x 4 = 20 years
Haroon’s present age = 7 x 4 = 28 years
Q 10: The number of boys
and girls in a class are in the ratio of 7 : 5. The number of boys is 8 more
than the number of girls. What is the total class strength?
Solution: (taking hint from Q.9 try to
solve this question yourself.)
Q 11: Baichung’s father is
26 years younger than Baichung’s grandfather and 29 years older than
Baichung’s. The sum of the ages of all the three is 135 years. What is the age
of each one of them?
Solution:
Let Baichung’s age = x years.
Baichung’s father’s age = x + 29 years
Baichung’s grandfather’s age = x + 29 + 26 = x +55 years
Given that sum of the ages of all three
persons = 135 years.
or, x + x + 29 + x + 55 = 135
or, 3x + 84 = 135
or, x
= 17
Hence, Baichung’s age = 17 years.
Baichung’s father’s age = 17 + 29 = 46
years
Baichung’s grandfather’s age = 17 + 29
+ 26 = 72 years
Q 12: Fifteen years from
now Ravi’s age will be 4 times his present age. What is Ravi’s present age?
Solution:
Let Ravi’s present age = x years
15 years later Ravi’s age will be x + 15 years
According to the given condition,
4x
= x + 15
or, x
= 5 years
Hence, Ravi’s present age = 5 years.
Q 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?
Solution:
Let the number be x.
Q 14: Lakshmi is a cashier
in a Bank. She has currency notes of denominations Rs. 100, Rs. 50 and Rs. 10
respectively. The ratio of the number of these notes is 2 : 3 : 5. The total
cash with Lakshmi is Rs. 4,00,000. How many notes of each denomination does she
have?
Solution:
Let the currency notes are in the
ratios of x.
(a) Number of Rs 100 notes = 2x and
its value = Rs 100 x 2x = Rs 200x.
(b) Number of Rs 50 notes = 3x and
its value = Rs 50 x 3x = Rs 150x.
(c) Number of Rs 10 notes = 5x and
its value = Rs 10 x 5x = Rs 50x.
Given the total value of all notes =
4,00,000
or, 200x + 150x + 50x = 400000
or, x
= 1000
Therefore,
Number of Rs 100 notes = 2 x 1000 =
2000
Number of Rs 50 notes = 3 x 1000 = 3000
Number of Rs 10 notes = 5 x 1000 =
5000.
Q 15: I have a total of Rs
300 in coins denomination Rs 1, Rs 2 and Rs 5. The number of Rs 2 coins is
three times the number of Rs 5 coins. The total number of coins is 160. How
many coins of each denomination are with me?
Solution:
Let the number of Rs 1 coins be x and its value then Rs x,
Number of Rs 5 coins be y and its value then Rs 5y,
Number of Rs 2 coins be 3y and its value then Rs 6y
(since it is given that the number of
Rs 2 coins is three times the number of Rs 5 coins).
Now, x + y + 3y = 160 (given that total number of
coins = 160) . . . (i)
x + 5y + 6y = 300 (given that
total value Rs 300) . . . . (ii)
Solving equations (i) and (ii) we
obtain,
x = 80 and y =
20
Therefore, number of Rs 1 coins = 80
Number of Rs 5 coins = 20
Number of Rs 2 coins = 60
Q 16: The organizers of an
essay competition decide that a winner in the competition gets a prize of Rs
100 and a participant who does not win gets a prize of Rs 25. The total prize
money distributed is Rs 3000. Find the number of winners, if the total number
of participants is 63.
Solution:
The total number of participants = 63.
Let the number of winner be x.
Winners get Rs 100x.
Number of participants who does not win
= 63 – x.
They get Rs (63 – x) x 25.
Now as per the given conditions,
100x
+ (63 – x) x 25 = 3000
or, 75x + 1575 = 3000
or, x
= Number of winners = 19.
View
solutions for Question No.1 - 8
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