Question

The age of Ashwini's mother is 5years more Than twice of Ashwini's Age. After 10 years, her mother's age will be 08 years less than thrice her age. Find their present age

Answer 1

Answers

✩ Present age of Ashiwini = 23  years .

✩ Present age of Ashiwini's mother = 51 years.

SOLUTION

Let us Assume that the Present age of Ashiwini as 'x' years.

Case :- 1

The age of Ashwini's mother is 5years more Than twice of Ashwini's Age.

$\implies$

The Present age of Ashwini's mother = 2x + 5 $\longrightarrow$(1)

Case :- 2

After 10 years, her mother's age will be 08 years less than thrice her age.

$\implies$

Age of Ashwini's mother after 10 years = 3x - 8$\longrightarrow$(2)

We have found in (1) that the present age of Ashwini's mother is 2x + 5 , so after 10 years it will be

2x + 5 + 10 = 2x + 15 $\longrightarrow$(3)

Now, Let us equate Equations (2) and (3)

$\implies$

2x + 15 = 3x - 8

$\implies$

3x - 2x = 15 + 8

$\implies$

x = 23 years

Present age of  Ashiwini (x) = 23 years.

Now , we can find the present age of Ashwini's mother by substituting 'x' as 23 in Equation (1) .

$\implies$

The Present age of Ashwini's mother = 2 × 23 + 5

$\implies$

The Present age of Ashwini's mother = 46 + 5

$\implies$

The Present age of Ashwini's mother =  51 years.