Question

21. The ages of Asha and Nirmala are in the ratio of 5:6 Five years from new, their ages will be 6:7. Find their present ages.​

Answer 1

SoluTion:

Let present age of asha be 5x and present age of nirmala be 6x.

According to the question,

Five years from now, the ratio of their ages will be 6:7

• Age of asha five yrs from now = 5x - 5
• Age of nirmala five yrs from now = 6x - 5

→ (5x - 5)/(6x - 5) = 6/7

→ 7(5x - 5) = 6(6x - 5)

→ 35x - 35 = 36x - 30

→ 35x - 36x = -30 + 35

→ -x = 5

Age can't be negative so we'll take positive value.

As we supposed

★ Age of asha = 5x

→ Age of asha = 5 × 5

→ Age of asha = 25 years

★ Age of nirmala = 6x

→ Age of nirmala = 6 × 5

→ Age of nirmala = 30 years

Hence, present ages of asha and nirmala will be 25 years and 30 years respectively.

Answer 2

Answer:

let Asha's present age=x

let Nirmal's present age = y

therefore, x:y = 5:6

let common multiple be k

then, x=5k and y=6k

and,

Asha's age 5 years from now = x+5

Nirmal's age 5 years from now= y+5

therefore,

$\frac{x + 5}{ y + 5} = \frac{6}{7}$

$\frac{5k+5}{ 6k+5} = \frac{6}{7}$

5k+35= 36k+30

or, k=5

therefore,

Present age of Asha=25 and Nirmal= 30