Oh! Its not the age to solve this , a small child can do this

Algebra Level 1

If the ratio of Sonal and Raj ages is 2:3 respectively and sum of their ages are 20 years.Then what will be the difference of their ages after 12 years.


The answer is 4.

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2 solutions

S = age of Sonal at present

R = age of Raj at present

S R = 2 3 \dfrac{S}{R}=\dfrac{2}{3} \implies 3 S = 2 R 3S=2R ( 1 ) (1)

S + R = 20 S+R=20 \implies S = 20 R S=20-R ( 2 ) (2)

Substitute ( 2 ) (2) in ( 1 ) (1) ,

3 ( 20 R ) = 2 R 3(20-R)=2R \implies 60 3 R = 2 R 60-3R=2R \implies 60 = 5 R 60=5R \implies R = 12 R=12

It follows that S = 20 12 = 8 S=20-12=8

The difference of their ages 12 years from now is equal to the difference of their ages at present. So the desired answer is 12 8 = 4 12-8=\boxed{4}

Shubham Joshi
Jul 20, 2015

let ages be 2x and 3x..... Now 2x + 3x = 20, 5x=20 ,x=4 Now, 2 X 4 = 8 and 3 X 4 = 12...after 12 years 8 + 12 = 20 and 12 +.12 = 24.Now, differnece 24- 20 = 4 (answer)

Shouldn't the difference be 24 - 20 = 4 instead of 24 - 12 = 4 ? Also, there is no need to calculate the ages after 12 years, as the difference will remain the same, that is, 12 - 8 = 4 Worth a thought !

Dhaval Furia - 5 years, 10 months ago

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yaa you are correct. The difference will remain same but I have to do all the steps mentioned in the questions or else people will tell me that you have not done all the steps mentioned there . Also sorry for that 24 - 12 mis typing.......

Shubham Joshi - 5 years, 10 months ago

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Good problem.

A Former Brilliant Member - 3 years, 2 months ago

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