Question

The ages of two persons A and B are in the ratio 7:5 .Ten years hence,the ratio of their ages will be 9:7.Find their ages.

Answer 1

$\boxed{\bold{\large{Answer:}}}$

$\text{Let\:the\:present\:age\:of\:A\:=\:7x\:years}$

$\text{Present\:age\:of\:b\:=\:5x\:years}$

$\text{After\:10\:years\:their\:ages\:will\:be,}$

$A = (7x + 10) \: years \\ \\ B = (5x + 10) \: years$

$\text{According\:to\:the\:Question,}$

$\implies \frac{(7x + 10)}{(5x + 10)} = \frac{9}{7} \\ \\ \implies49x + 70 = 45x + 90 \\ \\ \implies49x - 45x = 90 - 70 \\ \\ \implies4x = 20 \\ \\ \implies \: x = \frac{20}{4} \\ \\ \implies \: x = 5$

$\text{Thus,}$

$\text{Present\:age\:of\:A\:=\:7x\:=\:7\:x\:5\:=\:35\:Years}$

$\text{Present\:Age\:of\:B\:=5x\:=\:5\:x\:5\:=\:25\:Years}$

$\boxed{\bold{\large{Hope\:it\:helps\:you!}}}$

Answer 2

let Leena's present age be 7x years and Heena's present age be 5x years            
 After 10 years,
Leena's age=7x+10
Heena's age=5x+10
7x+10+5x+10=9x+7x
20=16x-12x
20=4x
x=5

Leena's present age=7x=7×5=35
Heena's present age=5×5=25