Question

The present ages of Rohit and Mayank 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 Rohit and Mayank are in the ratio 11 : 8. 8 years later the sum of their ages will be 54 years.

To Find :-

What are their present ages?

Let :-

Present age of Rohit = 11x

Present age of Mayank = 8x

Ages after 8 years,

Rohit age = 11x + 8

Mayank age = 8x + 8

By the question,

(11x + 8) + (8x + 8) = 54

➟ 11x + 8 + 8x + 8 = 54

➟ 19x + 16 = 54

➟ 19x = 54 - 16

➟ 19x = 38

➟ x = 2

Hence,

• Present age of Rohit = 11x = 11 × 2 = 22 years
• Present age of Mayank = 8x = 8 × 2 = 16 years

Answer 2

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Given: Rohit & Mayank's present ages are in the ratio 11:8, after 8 years the sum of their ages will be 54 years

To find: Rohit & Mayank's present ages

Consider Rohit and Mayank's present ages to be 11x and 8x, so the ratio of their ages is 11:8.

After 8 years, their ages will be(11x + 8) and (8x + 8).

So, according to the question, the linear equation is given by -

(11x + 8) + (8x + 8) = 54

Calculate value of x using equation -

✒(11x + 8) + (8x + 8) = 54 x = 2

✒19x + 16 = 54

✒19x = 54 - 16

✒x = 38/19

Hence,when Rohit & Mayank's present ages are in the ratio 11:8 and after 8 years the sum of their ages will be 54 years, then

✒Rohit's present age is 22 years and

✒Mayank's present age is 16 years.