Question

. The ratio of the present ages of Surya and Deepa is
5:6. Twelve years ago, the ratio of of the age of
1th
2
1th
4
Surya and of age of Deepa was 3 : 2. What will
be the ratio of the ages of Surya and Deepa
18 years hence?
(1) 3:4 (2) 4:3
(3) 9:8
(4) 8:9 (5) None of these​

Answer 1

Correct Question :

The ratio of present ages of Surya and Deepa is 6:5 . 12 years ago, the ratio of the age of Surya and Deepa was 3:2. What will be the ratio of the ages of Surya and Deepa 18 years hence ?

Given :

• The ratio of present ages of Surya and Deepa is 6:5.
• 12 years ago, the ratio of the age of Surya and Deepa was 3:2.

To find :

• 18 years hence , the ratio of the ages of Surya and Deepa.

Solution :

Let the present age of Surya be 6x years and the present age of Deepa be 5x years.

12 years ago,

• Age of Surya = (6x-12) years.
• Age of Deepa = (5x-12) years.

According to the question :-

• 12 years ago, the ratio of the age of Surya and Deepa was 3:2.

$\implies\sf{(6x-12):(5x-12)=3:2}$

$\implies\sf{\dfrac{6x-12}{5x-12}=\dfrac{3}{2}}$

$\implies\sf{15x-36=12x-24}$

$\implies\sf{15x-12x=36-24}$

$\implies\sf{3x=12}$

$\implies\sf{x=4}$

Now put the value of x = 4 for getting the present age of Surya and Deepa.

★ Present age of Surya = 6×4 = 24 years.

★ Present age of Deepa = 5×4 = 20 years.

After 18 years,

• Age of Surya = (24+18) = 42 years.
• Age of Deepa = (20+18) = 38 years.

Ratio of their ages after 18 years ,

→ 42 : 38

→ 21:19

Therefore, after 18 years, the ratio of their ages will be 21:19.