Question
The present ages of Arun and Varun are in the ratio 1:2. 5
years ago, the average age of Arun, Varun, and Kiran was 25 years. At that time, Arun was 10 years younger than Kiran. What will be Kiran’s age 10 years from now?Solution
ATQ,
Let present ages of Arun and Varun be x and 2x, and Kiran’s present age be y years.
5 years ago:
Arun = x – 5
Varun = 2x – 5
Kiran = y – 5
ATQ,
(x – 5 + 2x – 5 + y – 5) = 3 × 25
⇒ 3x + y – 15 = 75
⇒ 3x + y = 90 ----------- (I)
Also,
x = y – 10 ⇒ y – x = 10 ------------ (II)
Subtracting (II) from (I):
3x + y – (y – x) = 90 – 10
⇒ 4x = 80
⇒ x = 20
Putting x = 20 in (I):
3×20 + y = 90 ⇒ y = 30
Kiran’s age 10 years from now = 30 + 10 = 40 years
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