Question

10. The ratio of Reema's age to Sudha's age is 1 : 5. Ten
years later, the ratio of their ages will be 3: 7. Find
their present ages.​

Answer 1

The ratio of Reema and Sudha's age is 1:5

Let x be the common multiple

Hence, Reema's Present age-1x

Sudha's Present age-5x

After ten years their ages will be

(1x+10) and (5x+10)

and the ratio of their ages will be 3:7

•(x+10) : ( 5x+10) = 3:7

Cross multiply

(x+10)7 =(5x+10)3

7x + 70=15x +30

15x-7x = 70x - 30x

8x = 40

x=40÷ 8

• x =5

•Reema's present age is 1x=5 years Sudha's Present age is 5x=5×5=25 years

Answer 2

Given:

• Ratio of Reema's age to Sudha's age is 1:5.
• Ten years later, the ratio of their ages will be 3:7.

To find:

• Present age of Reema and Sudha?

Solution:

☯ Let the present age of Reema and Sudha be x and y respectively.

★ According to the Question:

• Ratio of Reema's age to Sudha's age is 1:5.

➻ x/y = ⅕

➻ 5x = y

➻ y = 5x⠀⠀⠀⠀⠀ ❲ eq (1) ❳

And,

• Ratio of Reema's age to Sudha's age after 10 years will be 3:7.

➻ (x + 10)/(y + 10) = 3/7

➻ 7(x + 10) = 3(y + 10)

➻ 7x + 70 = 3y + 30

➻ 7x - 3y = 30 - 70

➻ 7x - 3y = - 40⠀⠀⠀⠀⠀ ❲ eq (2) ❳

⠀━━━━━━━━━━━━━━━━━━━

Now, Substituting eq (1) in eq (2),

➻ 7x - 3(5x) = - 40

➻ 7x - 15x = - 40

➻ - 8x = - 40

➻ x = 40/8

➻ x = 5

Now, Substituting value x in eq (1),

➻ y = 5 × 5

➻ y = 25

Therefore,

• Present age of Reema, x = 5 years
• Present age of Sudha, y = 25 years

∴ Hence, the present age of both Reema and Sudha is 5 years and 25 years respectively.