Question

the age of two girls are in the ratio 5:7. eight years ago their ages were in the ratio 7:13.find their present ages​

Answer 1

SoluTion:

Let age of first and second girl be 5x and 7x respectively.

Eight years ago,

→ Age of first girl = 5x - 8

→ Age of second girl = 7x - 8

According to question,

→ (5x - 8)/(7x - 8) = 7/13

→ (5x - 8)13 = (7x - 8)7

→ 65x - 104 = 49x - 56

→ 65x - 49x = -56 + 104

→ 16x = 48

→ x = 48/16

→ x = 3

Their present ages,

★ Present age of first girl = 5x

→ Present age of first girl = 5 × 3

→ Present age of first girl = 15 years

★ Present age of second girl = 7x

→ Present age of second girl = 7 × 3

→ Present age of second girl = 21 years

Answer 2

Given :

• Age of two girls are in the ratio of 5:7
• Eight years ago their ages were in the ratio of 7:13

To find :

• Their present ages

According to the question,

Let the ratio be 5x and 7x

Eight years ago,

• 1st girl age will be 5x - 8
• 2nd girl age will be 7x - 8

So,the equation will be

$\sf{ \: \: : \implies \frac{5x - 8}{7x - 8} = \frac{7}{13} }$

$\sf{ \: \: : \implies 13(5x - 8) = 7(7x - 8)}$

$\sf{ \: \: : \implies 65x - 104 = 49x - 56}$

$\sf{ \: \: : \implies 65x -49x= - 56 + 104}$

$\sf{ \: \: : \implies 16x = 48}$

$\sf{ \: \: : \implies x = \cancel\frac{48}{16} {}^{ \: \: 3} }$

$\sf{ \: \: : \implies x = 3 } \: \orange \bigstar$

_____________....

So,

Present age of 1st girl = 5x = 5 × 3 = 15 years...

Present age of 2nd girl = 7x = 7 × 3 = 21 years...