Question

the ages of Rishit and Ashmit are in the ratio 3:5 . five years later the sum of their ages will be 26 what are their present ages​

Answer 1

$\bf{\huge{\underline{\boxed{\rm{\red{Answer:}}}}}}$

Given:-

• the ages of Rishit and Ashmit are in the ratio 3:5
• five years later the sum of their ages will be 26

Let x be the common multiple of the ratio , 3 : 5

•°• Rishit = 3x years.

Ashmit = 5x years.

As per the question,

• five years later the sum of their ages will be 26,

5 years later, their present age will be,

Rishit = 3x + 5 years

Ashmit =5x + 5 years

Sum of their ages = 26

(3x + 5) + (5x + 5) = 26

3x + 5 + 5x + 5 = 26

3x + 5x + 5 + 5 = 26

8x + 10 = 26

8x = 26 - 10

8x = 16

x = $\bf\large\frac{16}{8}$

x = 2

Value of common multiple, x = 2

Substitute the value of x, in ages of Rishit and Ashmit to find their present ages.

$\bf{\large{\underline{\boxed{\rm{\red{Rishit = 3x = 3 × 2 = 6 years. }}}}}}$

$\bf{\large{\underline{\boxed{\rm{\blue{ Ashmit = 5x = 5 × 2 = 10 years}}}}}}$

$\bf{\huge{\underline{\boxed{\rm{\pink{Verification:}}}}}}$

For first case :-

• the ages of Rishit and Ashmit are in the ratio 3:5

Age of Rishit = 6 years.

Age of Ashmit = 10 years.

The ratio of their ages, 6 : 10

$\bf\large\frac{6}{10}$ = $\bf\large\frac{3}{5}$

Dividing by 2 on the LHS,

$\bf\large\frac{3}{5}$ = $\bf\large\frac{3}{5}$

LHS = RHS.

For second case :-

• five years later the sum of their ages will be 26

5 years later,

Age of Rishit = 3x + 5 = 3 × 2 + 5 = 11

Age of Ashmit = 5x + 5 = 5 × 2 + 5 = 15

Sum of their ages = 26,

11 + 15 = 26

26 = 26

LHS = RHS.

Hence, concluding that our answer is right.