Question

The ratio of ages of Ram and Hari is 2:1 and difference of
their ages is 20 years. Find their present ages.
​

Answer 1

Given :

• The ratio of ages of Ram and Hari is 2:1.
• Difference of their ages is 20 years.

To find :

• Their present ages =?

Step-by-step explanation :

Let the present age of Ram's be, 2x.

Then, the present age of Hari's be 1x.

It is Given that,

Difference of their ages is 20 years.

As per question,

2x - 1x = 20

x = 20.

Therefore, We got the value of, x = 20.

Hence,

The present age of Ram's, 2x = 2 × 20 = 40 year's .

Then, the present age of Hari's 1x = 1 × 20 = 20 years .

Answer 2

Let the present ages of Ram & Hari be x & y respectively.

Then,

$\: \: \: \: \: \bf \frac{x}{y} = \frac{2}{1} \: \: \: \\ \bf= > \: x = 2y \: \: \: \: \: \: \: \: - - - \\ \boxed{ \bf = > x - 2y = 0 \: \: \: \: \: \: - - (1)}\\ \\ \boxed{\bf{x - y = 20} \: \: \: \: \: \: \: \: \: - - - (2)}$

On subtracting eq (2) from eq (1), we get,

$\tt \cancel{x} - 2y \: \cancel{- x} + y = 0 - 20 \\ \tt = > (- 2 + 1)y = - 20 \\ \tt = > - (1)y = - 20 \\ \sf = > y = \frac{ - 20}{ - 1} = \red{20} \: yrs$

Now,

$\huge \sf \: {x = 2(y)} \\ \sf= > \: \: x = 2(20) = \red{40} \: yrs$

Heñce,

• Age of Ram = 40 years
• Age of Hari = 20 years