Question

The present ages of Raj and Maanik are in the ratio 11:8. 8 years later the sum of their ages will be 54 years. What are their present ages?

Answer 1

Given :

• The present ages of Raj and Maanik are in the ratio 11:8.

• 8 years later the sum of their ages will be 54 years.

To find :

• Their present ages =?

Step-by-step explanation :

Let, the present age of Raj's be 11x.

Then, the present age of Maanik's be 8x.

8 years later Raj's age will be, 11x + 8

8 years later Maanik's age will be, 8x + 8

According to the question :

➮ (11x + 8) + ( 8x + 8) = 54

➮ 11x + 8 + 8x + 8 = 54

➮ 11x + 8x + 8 + 8 = 54

➮ 19x + 16 = 54

➮ 19x = 54 - 16

➮ 19x = 38

➮ x = 38/19

➮ x = 2

Therefore, We got the value of, x = 2.

Hence,

The present age of Raj's, 11x = 11 × 2 = 22 year's

The present age of Maanik's, 8x = 8 × 2 = 16 years

Answer 2

Answer:

Let the Present Age of Raj be 11n and Present Age of Maanik be 8n.

⠀

☢ Given : Sum of Ages of Both after 8 years will be 54 Years.

⠀

☯ $\underline{\boldsymbol{According\: to \:the\: Question :}}$

$:\implies\sf (Raj+8)+(Mannik+8)=54\\\\\\:\implies\sf (11n+8)+(8n+8)=54\\\\\\:\implies\sf 11n+8+8n+8=54\\\\\\:\implies\sf 19n+16=54\\\\\\:\implies\sf 19n=54-16\\\\\\:\implies\sf 19n=38\\\\\\:\implies\sf n=\dfrac{38}{19}\\\\\\:\implies\sf n=2$

⠀⠀⠀$\rule{160}{1}$

$\bullet\:\:\textsf{Raj = 11n = 11(2) = \textbf{22 years}}\\\bullet\:\:\textsf{Maanik = 8n = 8(2) = \textbf{16 years}}$