Question

The ratio of present ages of Rahul and his sister is 3 : 4. Before 10 years the ratio of their ages was 13:19. What is Rahul's present age (in years)?

A) 36 B) 48 C) 42 D) 54

Answer 1

Given :

Ratio of present ages of Rahul and his sister = 3:4 .

Ratio of ages 10 years before = 13:19

To find :

Present age of Rahul .

Solution:

Let the common ratio be x .

Hence , present age of Rahul = 3x

Present age of sister = 4x .

10 years before ,

Rahul's age = 3x - 10

Sister's age = 4x - 10

According to question , before ten years

Rahul's age = 13x

Sister's age = 19 x

Dividing and equating equations of 10 years before ,

$\rm \: \frac{3x - 10}{4x - 10} = \frac{13x}{19x}$

By cross multiplication

$\rm \implies 19x(3x - 10) = 13x(4x - 10)$

$\rm \implies \: 57 {x}^{2} - 190x = 52 {x}^{2} - 130x$

$\rm \implies 57 {x}^{2} - 52 {x}^{2} = - 130x + 190x$

$\rm \implies 5 {x}^{2} = 60x$

$\rm \implies x = \frac{60x}{5x}$

$\rm \implies x = 12$

Rahul's present age = 3x

= 3 × 12

$\therefore \boxed{\rm{\large{\orange{Rahul's\ present\ age = 36\ years}}}}$

Answer 2

${ \huge{ \bold{ \underline{ \underline{ \blue{Question:-}}}}}}$

The ratio of present ages of Rahul and his sister is 3 : 4. Before 10 years the ratio of their ages was 13:19. What is Rahul's present age (in years)?

A) 36 B) 48 C) 42 D) 54

______________________

${ \huge{ \bold{ \underline{ \underline{ \purple{Answer:-}}}}}}$

• Let Present age of Rahul be = 3x
• Let Present age of his sister be =4x

✎10 years Ago :

• Rahul age was = 3x - 10
• His sister age was = 4x - 10

✎Ratio of their ages before 10 years :

• Rahul age = 13x
• Sister age = 19x

✎Now,

$\implies{\dfrac{3x-10}{4x-10}=\dfrac{13x}{19x}}$

✎On Calculating :

$\implies{19x(3x-10) =13x(4x-10)}$

$\implies{{57x}^{2}-190x={52x}^{2}-130x}$

$\implies{{57x}^{2}-{52x}^{2}=-130x+190x}$

$\implies{{5x}^{2}=60x}$

$\implies{x=\dfrac{60x}{5x}}$

$\implies{{ \large{ \bold{ \bold{ \bold{ \orange{x=12}}}}}}}$

✎So,

$\implies{Rahul\:present\:age=3x}$

$\implies{3(12) }$

$\implies{36\:years}$

$\implies{His\:sister\:age=4x}$

$\implies{4(12)}$

$\implies{48\:years}$