Question

The ratio of the ages of Ram and Gopal is 3:4. The difference between their ages after two years will be 10. How old are they? Answer is 40 and 30

Answer 1

Answer:

Present age of Ram is 30 years and Gopal is 40 years.

Step-by-step explanation:

Let,

Present age of Ram be 3a years.

Present age of Gopal be 4a years.

After 2 years :

= > Age of Ram = Present age of Ram + 2 years

= 3a years + 2 years

= ( 3a + 2 ) years

= > Age of Gopal = Present age of Gopal + 2 years

= 4a years + 2 years

= ( 4a + 2 ) years

According to the question :

= > Age of Gopal after 2 years - age of Ram after 2 years = 10 years

= > ( 4a + 2 ) years - ( 3a + 2 ) years = 10 years

= > ( 4a + 2 ) - ( 3a + 2 ) = 10

= > 4a - 3a + 2 - 2 = 10

= > a = 10

Hence,

Present age of Ram = 3a years = 3( 10 ) years = 30 years

Present age of Gopal = 4a years = 4( 10 ) years = 40 years.

Thus the present age of Ram is 30 years and Gopal is 40 years.

Answer 2

• Let present age of Ram be 3M and present age of Gopal be 4M.

» $\underline{After\: two \:years}$

Age of Ram = 3M + 2

Age of Gopal = 4M + 2

» And the difference of their (Ram and Gopal) ages is 10

• A.T.Q.

$\implies$ (4M + 2) - (3M + 2) = 10

$\implies$ 4M + 2 - 3M - 2 = 10

$\implies$ $\boxed{M \:= \:10}$

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$\textbf{Present age of Ram}$ = 3M = 3 × 10 = $\textbf{30 years}$

$\textbf{Present age of Gopal}$ = 4M = 4 × 10 = $\textbf{40 years}$

_____________ $\bold{[ANSWER]}$

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