Question

the present ages of anmol and Supriya are in the ratio 2 : 3. 10 years from now their ages will be in the ratio 3 : 4

Answer 1

$\bf{\underline{\huge{\boxed{\sf{\green{Answer:}}}}}}$

Correct question :-

• The present ages of anmol and Supriya are in the ratio 2:3. Ten years from now their ages will be in the ratio 3 : 4. Find their present age.

$\bf{\underline{\underline{\rm{\red{Given:}}}}}$

• The present ages of Anmol and Supriya are in the ratio 2 : 3
• 10 years from now their ages will be in the ratio 3 : 4

$\bf{\underline{\underline{\rm{\red{To\:find:}}}}}$

• Present age of Anmol
• Present age of Supriya

$\bf{\underline{\underline{\rm{\red{Solution:}}}}}$

Let x be the common multiple of the ratio 2:3

•°• Anmol's present age = 2x

Supriya's present age = 3x

$\bf{\underline{\underline{\rm{\red{As\:per\:the\:question:}}}}}$

• 10 years from now their ages will be in the ratio 3 : 4

Ages after 10 years from now :-

Anmol's age = 2x + 10

Supriya's age = 3x + 10

Ratio = 3:4

Representing it mathematically,

=> $\bf\large\frac{2x+10}{3x+10}$ = $\bf\large\frac{3}{4}$

Cross multiplying,

=> 4 ( 2x + 10) = 3 ( 3x + 10)

=> 8x + 40 = 9x + 30

=> 8x - 9x = 30 - 40

=> - x = - 10

=> $\cancel{-}$ x = $\cancel{-}$ 10

=> x = 10

Substitute x = 10 in the values of the ratio.

$\bf{\underline{\large{\boxed{\sf{\pink{Present\:age\:of\:Anmol\:=\:2x\:=\:2\times\:10\:=\:20\:years}}}}}}$

$\bf{\underline{\large{\boxed{\sf{\pink{Present\:age\:of\:Supriya\:=\:3x\:=\:2\times\:10\:=\:30\:years}}}}}}$

$\bf\huge\underline{Verification:}$

For first case :-

• The present ages of Anmol and Supriya are in the ratio 2 : 3

Anmol's age = 20 years

Supriya's age = 30 years

Ratio = 2 : 3

=> $\bf\large\frac{20}{30}$ = $\bf\large\frac{2}{3}$

Dividing LHS by 10,

=> $\bf\large\frac{2}{3}$ = $\bf\large\frac{2}{3}$

LHS = RHS.

For second case :-

• 10 years from now their ages will be in the ratio 3 : 4

Ages after 10 years :-

Anmol's age = 2x + 10 = 20 + 10 = 30 years

Supriya's age = 3x + 10 = 30 + 10 = 40 years

Ratio = 3:4

=> $\bf\large\frac{2x+10}{3x+10}$ = $\bf\large\frac{3}{4}$

=> $\bf\large\frac{30}{40}$ = $\bf\large\frac{3}{4}$

Dividing LHS by 10,

=> $\bf\large\frac{3}{4}$ = $\bf\large\frac{3}{4}$

LHS = RHS.

Hence verified.