Question

9. The ages of Rahul and Haroon are in the ratio 5:7. Four years later the sum of their
ages will be 56 years. What are their present ages?
​

Answer 1

(5x+4) + (7x+4) = 56

⇒ 5x + 7x + 4 + 4 = 56

⇒ 12x + 8 = 56

⇒ 12x = 56 - 8

⇒ 12x = 48

⇒ x = 48/12 = 4

⇒ age of Rahul = 5x = 5(4) = 20 years

 ⇒ age of Haroon = 7x = 7(4) = 28 years

Answer 2

${ \underline{ \underline {\large \red{ \star} \color{blue}{ \textsf {\textbf{ Given :}}}}}}$

• The ages of Rahul and Haroon are in the ratio 5:7. Four years later the sum of their ages will be 56 years.

${ \underline{ \underline {\large \red{ \star} \color{blue}{ \textsf {\textbf{ To \: Find :}}}}}}$

• Present ages?

${ \underline{ \underline {\large \red{ \star} \color{blue}{ \textsf {\textbf{ Solution :}}}}}}$

• Let present age of Rahul be 5x,
• Present age of Haroon be 7x

★4 years later:

• Age of rahul = (5x + 4)
• Age of Horron = (7x + 4)

★According to Question,

$\sf :\implies(5x + 4) (7x + 4) = 56 \\ \\ \\ \sf :\implies5x + 7x + 4 + 4 = 56 \\ \\ \\ \sf :\implies12x + 8 = 56 \\ \\ \\ \sf :\implies12x = 56 - 8 \\ \\ \\ \sf :\implies x = 48 \\ \\ \\ \sf :\implies x = \frac{48}{12} \\ \\ \\ \sf :\implies x = 4$

$\: { \underline{ \underline {\red{\star}{ \textsf{ \textbf{Present \: ages: }}}}}}$

• Age of Rahul = 5x = 20 years

• Age of Haroon = 7x = 28 years.

_____________________________________