2
votes

The ratio of ages of the father and his son at present is $12 : 5$, the difference of their age is $28$ years. What will be the ratio of their ages after eight years ?

- $2:2$
- $3:1$
- $2:1$
- $3:2$

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2
votes

The ratio of ages of the father and his son at present is $12 : 5$, the difference of their age is $28$ years. What will be the ratio of their ages after eight years ?

- $2:2$
- $3:1$
- $2:1$
- $3:2$

See all

Best answer

1
votes

The present age of father and son at present is $12x$ years and $5x$ years respectively.

Now, $12x – 5x = 28$

$\implies 7x = 28$

$\implies x = 4$

$\therefore $ Father present age $ = 12x = 48$ years and son present age $ = 5x = 20$ years.

Now, the required ratio $ = \dfrac{48+8}{20+8} = \dfrac{56}{28} = \dfrac{2}{1}$

Hence, the ratio of their ages after eight years $ = 2:1.$

So, the correct answer is $(C).$

Now, $12x – 5x = 28$

$\implies 7x = 28$

$\implies x = 4$

$\therefore $ Father present age $ = 12x = 48$ years and son present age $ = 5x = 20$ years.

Now, the required ratio $ = \dfrac{48+8}{20+8} = \dfrac{56}{28} = \dfrac{2}{1}$

Hence, the ratio of their ages after eight years $ = 2:1.$

So, the correct answer is $(C).$

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