Question

Amit is 19 years younger than his father. After 5 years, their ages will be in the ratio of 2:3. Find their present ages.

Answer 1

Answer:

33 is answer present age is 33

Answer 2

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given that Amit is 19 years younger than his father
• After 5 years Amit age to his father would be in the ratio 2:3

To Find:

• We have to find the present age of Amit and his father

Solution:

Let present age of Father = x

Present age of Amit = ( x - 19 )

After 5 years

Age of Father = ( x + 5 )

Age of Amit = ( x - 19 + 5 ) = ( x - 14 )

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$\underline{\large\mathfrak\orange{According \: to \: the \: Question:}}$

$\implies \sf{\dfrac{x-14}{x+5} = \dfrac{2}{3}}$

Cross Multiplying the terms

$\implies \sf{3(x-14) = 2(x+5)}$

$\implies \sf{3x - 42 = 2x + 10}$

$\implies \sf{3x - 2x=10+42}$

$\implies \boxed{\sf{x=52}}$

Age of Father = 52 years

Age of Amit = 52 - 19 = 33 years

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$\huge\underline{\sf{\red{A}\orange{n}\green{s}\pink{w}\blue{e}\purple{r}}}$

$\large\boxed{\sf{\red{Age \: of \: Amit = 33 \: Years}}}$

$\large\boxed{\sf{\purple{Age \: of \: Father = 52 \: Years}}}$

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$\huge\mathfrak\green{Verification:}$

1) Amit is 19 year younger than father

$\implies \sf{(Age \: of \: Father ) - 19}$

$\implies \sf{52 - 19}$

$\implies \sf{33 \qquad (Amit's \: age)}$

2) After 5 years Their age is in ratio 2:3

$\implies \sf{Ratio = \dfrac{33 + 5}{52+5}}$

$\implies \sf{\dfrac{38}{57}}$

$\implies \boxed{\sf{Ratio = \dfrac{2}{3}}}$

Hence Verified !!!

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