Question

the present age pf a and b are in the ratio 7:5 and 10 years later their age will be in the ratio 9:7 find the present age
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Answer 1

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*Answer:

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Let the present age of A= 7x years

The present age of B= 5x years

After 10 years, their ages will be

A=7x+10 years and

B=5x+10 years

The ratio of their ages after 10 years is 9:7

Hence ,

$= > \frac{7x + 10}{5x + 10} = \frac{9}{7}$

$= > \: 49x + 70 = 45x + 90 \\ = > 49x - 45x = 90 - 70 \: \\ = > 4x = 20 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$= > x = \frac{20}{4}$

$= > x \: = \: 5$

∴ Present age of A= 7×5=35 years

and

present age of B= 5×5=25 years.

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Answer 2

Answer :-

• Present Age of A = 35 years.

• Present Age of B = 25 years.

Explanation :-

Given :

• The present age of A and B are in the ratio 7:5.

• 10 years later, their age will be in the ratio 9:7.

To Find :

• Present Ages of A and B.

Solution :

Let the age of A be 7x and age of B be 5x.

$\bigstar$ According to the Question,

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

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

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

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

$\implies\sf{4x = 20 }$

$\implies\sf{x = \dfrac{20}{4} }$

$\implies\textsf{\textbf{x = \red{5} } }$

Therefore,

• Present Age of A = 7x = 35 Years.

• Present Age of B = 5x = 25 Years.