Question

the present ages of father and son are in the ratio 5:2. after 5 years, the ratio will be 7:3. the present age of the son is-
a)20years
b)30years
c)40years
d)50years​

Answer 1

Given

• The present ages of father and son are in the ratio 5:2.
• After 5 years, the ratio will be 7:3.

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To find

• Present age of the son.

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Solution

• Let the ratio be x.

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★ Present age of father = 5x

★ Present age of son = 2x

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After 5 years

★ Age of father will be = 5x + 5

★ Age of son will be = 2x + 5

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According to the question

$\tt:\implies\: \: \: \: \: \: \: \: {\dfrac{5x + 5}{2x + 5} = \dfrac{7}{3}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {3(5x + 5) = 7(2x + 5)}$

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$\tt:\implies\: \: \: \: \: \: \: \: {15x + 15 = 14x + 35}$

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$\tt:\implies\: \: \: \: \: \: \: \: {15x - 14x = 35 - 15}$

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$\tt:\implies\: \: \: \: \: \: \: \: {x = 20}$

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Therefore,

• Present age of son = 2 × 20 = 40 years.

Hence, option C is the correct option.

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