Question

32. The ratio between Sumit's and Prakash's deat
present is 2: 3. Sumit is 6 years younger than
Prakash. The ratio of Sumit's age to Prakash's age
after 6 years will be
(a) 2:3
(b) 1:2
(c) 4:3
(d) 3:4​

Answer 1

Answer:

Let Sumit's it's age be x years.

so Prakash's age will be (x+6) years.

So given : ratio is 2/3.

So x/(x+6) = 2/3

3x = 2x + 12

x = 12 years.

So Sumit's current age = 12 years.

Prakash's current age = 18 years.

After 6 years :

Sumit's age = 18 years.

Prakash's age = 24 years.

So ratio = 18/24 = 3/4.

So Option D is correct.

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Answer 2

Given : Ratio of Sumit's and Prakash's age is 2 : 3

            Sumit is 6 year younger than Prakash

To Find : Ratio of their age after 6 years.

Solution : Let Sumit's age be x years.

then,          Prakash's age will be (x+6) years.

                given  ratio is 2 : 3.

                 $\frac{x}{x + 6 } = \frac{2}{3}$          

                 $3x = 2x + 12$

                 $3x - 2x = 12$

                 $x = 12$ years

So, In present  Sumit's age = 12 years.

                    Prakash's  age = 18 years.

After 6 years , Sumit's age = 18 years.

                  Prakash's age  = 24 years.

                  $Ratio = \frac{18 }{24}$

                  $Ratio = \frac{3}{4}$ = 3 : 4

(d) option is correct i.e. 3 : 4

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