Question

The ages of Sonu and Monu are in the ratio 7:5 10 years from hence, the ratio of their ages will be 9:7 find their present ages.​

Answer 1

Answer:

Given :-

• The ages of Sonu and Monu are in the ratio of 7 : 5.
• 10 years from hence, the ratio of their ages will be 9 : 7.

To Find :-

• What is their present ages.

Solution :-

Let,

$\mapsto \rm{\bold{Present\: age\: of\: Sonu =\: 7x\: years}}$

$\mapsto \rm{\bold{Present\: age\: of\: Monu =\: 5x\: years}}$

$\clubsuit\: \: \sf\bold{\green{After\: 10\: years}}$

$\mapsto$ Age of Sonu = (7x + 10) years

$\mapsto$ Age of Monu (5x + 10) years

According to the question,

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

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

By doing cross multiplication we get,

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

$\implies \sf 49x + 70 =\: 45x + 90$

$\implies \sf 49x - 45x =\: 90 - 70$

$\implies \sf 4x =\: 20$

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

$\implies \sf x =\: \dfrac{5}{1}$

$\implies \sf\bold{\purple{x =\: 5\: years}}$

Hence, the required age of Sonu and Monu are :

$\bigstar\: \: \sf\bold{Present\: age\: of\: Sonu\: :-}$

$\longrightarrow \sf 7x\: years$

$\longrightarrow \sf 7(5)\: years$

$\longrightarrow \sf\bold{\red{35\: years}}$

$\bigstar\: \: \sf\bold{Present\: age\: of\: Monu\: :-}$

$\longrightarrow \sf 5x\: years$

$\longrightarrow \sf 5(5)\: years$

$\longrightarrow \sf\bold{\red{25\: years}}$

$\therefore$ The present age of Sonu and Monu is 35 years and 25 years respectively.

Answer 2

Given : The ages of Sonu and Monu are in the ratio of 7 : 5 & 10 years from hence, the ratio of their ages will be 9 : 7.

To Find : Find their present ages ?

_________________________

Solution : Let the present age be x.

$~$

• $\leadsto$Sonu as 7x
• $\leadsto$Monu as 5x

$~$

$\qquad{\sf:\implies{\dfrac{(7x + 10)}{(5x + 10)}~ = ~\dfrac{9}{7}}}$

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

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

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

$\qquad{\sf:\implies{4x~ = ~20}}$

$\qquad{\sf:\implies{x~=~\cancel\dfrac{20}{4}}}$

$\qquad:\implies{\underline{\boxed{\frak{\pink{x~=~5}}}}}$★

$~$

• Sonu's age

◗5 × 5

◗25

$~$

• Monu's age

◗7 × 5

◗35

$~$

Hence,

$\therefore\underline{\sf{The ~Present ~ages ~of~Sonu~and~Monu~is~\bf{\underline{35~years}}~\sf{\&}~\bf{\underline{25~years}}}}$