Question

The present ages of A and B are in the ratio 7:5.Ten years later,their ages will be in the ratio 9:7.find their present ages.​

Answer 1

Answer:-

Given:-

Ratio of present ages of A and B = 7 : 5.

Let,

A's present age be 7x years and B's present age be 5x years.

Also given that,

After 10 years , the ratio becomes 9 : 7.

According to above condition;

⟹ 7x + 10 : 5x + 10 = 9 : 7

⟹ 7(7x + 10) = 9(5x + 10)

⟹ 49x + 70 = 45x + 90

⟹ 49x - 45x = 90 - 70

⟹ 4x = 20

⟹ x = 20/4

⟹ x = 5

∴

• A's present age = 7x = 7(5) = 35 years.
• B's present age = 5x = 5(5) = 25 years.

Answer 2

Given :-

• Present Ages of A and B are in the Ratio 7:5.
• Ten years later,their ages will be in the ratio 9:7.

To Find :-

• Their Present Ages.

Solution :-

Let the of A = 7x years

Let the of B = 5x years

After 10 years their ages will be :-

• Age of A = 7x + 10
• Age of B = 5x + 10

★ According to the Question ★

${:} \longrightarrow \sf{\sf{\dfrac{7x \: + \: 10}{5x \: + \: 10}\: = \: \dfrac{9}{7} }}$

${:} \longrightarrow \sf{\sf{ 7(7x \: + \: 10) \: = \: 9(5x \: + \: 10) }}$

${:} \longrightarrow \sf{\sf{ 49x\: + \: 70 \: = \: 45x \: + \:90}}$

${:} \longrightarrow \sf{\sf{ 49x\: - \: 45x \: = \:90 \: - \: 70}}$

${:} \longrightarrow \sf{\sf{ 4x \: = \:20}}$

${:} \longrightarrow \sf{\sf{ x \: = \: \cancel \dfrac{20}{4}}}$

${:} \longrightarrow \sf{\bf{ x \: = \: 5}}$

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★ Their Present Ages ★

$\longmapsto \sf \: Present \: age \: of \: A \: = \: 7x \\ \longmapsto \sf \: Present \: age \: of \: A \: = \: 7 \: \times \: 5 \\ \longmapsto \bf \: Present \: age \: of \: A \: = \:35 \: years$

$\longmapsto \sf \: Present \: age \: of \: B \: = \: 4x \\ \longmapsto \sf \: Present \: age \: of \: B \: = \: 5 \: \times \: 5 \\ \longmapsto \bf \: Present \: age \: of \: B \: = \:25 \: years$

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