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

Step-by-step explanation:

let the number X

(7x+10)÷(5x+10)= 9/7

9(5x+10)= 7(7x+10)

45x+90= 49x+70

90-70=49x-45x

20=4x

5=X

their present ages are

5×7=35

5×5=25

Answer 2

⇝ Given :-

• 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

⇝ To Find :-

• Their Present Ages

⇝ Solution :-

As ages of A and B are in the ratio 7 : 5

Therefore Let,

• Present Age of A = $\rm{7x}$ years

• Present Age of B = $\rm{5x}$ years

❒ Ten Years Later :

• Age of A = $\rm{(7x+10)}$ years

• Age of B = $\rm{(5x+10)}$ years

⏩ According To Question :

$\large\red{ \rm \frac{7x + 10}{5x + 10} = \frac{9}{7}}$

$:\longmapsto \rm 7(7x + 10) = 9(5x + 10)$

$:\longmapsto \rm 49x + 70 = 45x + 90$

$:\longmapsto \rm 49x - 45x = 90 - 70$

$:\longmapsto \rm 4x = 20$

$:\longmapsto \rm x = \cancel\frac{20}{4}$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf x = 5} }}}$

Therefore,

Present Age of A = $\rm{7x}=7\times5$ = 35 years.

Present Age of B = $\rm{5x}=5\times5$ = 25 years.

Hence,

$\pink{\begin{cases} \bf Present  \:Age  \: of  \: A= 35 \:years \\  \\  \bf Present \:  Age \:  of \:  B = 25 \: years\end{cases}}$