# Question

If Benson is u years old now, his sister is 3u years old now.

In 12 years times , Benson will be u + 12 years old and his sister will be 3u + 12 years old.

Given Benson age : sister age = 2 : 3 in 12 years now,

3( u + 12 ) = 2( 3u + 12)

3u + 36 =  6u + 24

3u = 12

u = 4

Benson is 4 years old now.

Note: Checking, Benson is 4 yo, his sister is 12 yo now.

In 12 years time, Benson is 16 yo, his sister is 24.

16 * 3 = 48 = 24 * 2. Checked.

Benson/Sister = 2/3           Multiply both sides by 3 * sister

Benson * 3 = Sister * 2

Another way of looking at the ratio is Benson age is smaller, and his sister age is bigger in number. So if they are given in certain ratio, Benson’s age must be multiplied by bigger number to make the multiplication to be the same as his sister’ age multiplied by smaller ratio number.

How to get 3 and 2?

In 12 years times , Benson will be u + 12 years old and his sister will be 3u + 12 years old.

Given Benson age : sister age = 2 : 3 in 12 years now,

Mathematically,

Benson age/ sister age = 2/3

(u + 12)/ ( 3u + 12 ) = 2/3  Multiply both sides by 3(3u + 12)

(u + 12)/ ( 3u + 12 ) *  3(3u + 12)= 2/3 * 3(3u + 12)

3( u + 12 ) = 2( 3u + 12)

Hope this is clear.