RMO practice question 5

Algebra Level 5

Shivam and Medha are best friends. Shivam and Medha were comparing their ages and found that Medha is as old as Shivam was when Medha was as old as Shivam had been when Medha was half as old as Shivam is . If the sum of their present ages is 44 44 years , then Shivam's age is


The answer is 24.

Shivam Jadhav by Shivam Jadhav , 22, India

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3 solutions

Aditya Chauhan
Sep 10, 2015

Let us denote the present age of Shivam by x x and that of Medha by y y . Shivam is greater than Medha by x − y x-y years.

We start from the end of the sentence.

  1. The age of Shivam when Medha was half as old as Shivam is

Medha's age = x 2 \dfrac{x}{2}

So Shivam's age at that time will be = 3 x 2 − y \dfrac{3x}{2} - y

2.When Medha's age was = 3 x 2 − y \dfrac{3x}{2} - y

Shivam's age was = 5 x 2 − 2 y \dfrac{5x}{2} - 2y

This is equal to Medha's present age

5 x 2 − 2 y = y \dfrac{5x}{2} - 2y = y

5 x = 6 y 5x=6y

x + y = 44 x+y=44

Solving the two equations We get Shivam's age = x x = 24 \boxed{24}

Nice question Shivam Jadhav

5 Helpful 0 Interesting 0 Brilliant 0 Confused

I agree :)

Mehul Arora - 5 years, 9 months ago

Nice solution.

Chaitnya Shrivastava - 5 years, 9 months ago
Hana Wehbi
Jul 20, 2017

Nice problem, keep posting.

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Ramiel To-ong
Sep 11, 2015

nice solution

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