Question

Four years ago Ram was two times as old as Shyam, six years later from now; Ram will be only 1.5 times as old as Shyam. The present age of Ram and Shyam respectively will be-​

Answer 1

Given :

• 4 years ago , Ram was 2 times as old as Shyam.
• 6 years later from now, Ram will be only 1.5 times as old as Shyam.

To find :

• Present age of Ram & Shyam.

Solution :

Consider,

• Present age of Ram = x years
• Present age of Shyam = y years

According to the 1st condition :-

• 4 years ago , Ram was 2 times as old as Shyam.

4 years ago ,

• Age of Ram = (x-4) years
• Age of Shyam = (y-4) years

$\to\sf{x-4=2(y-4)}$

$\to\sf{x-4=2y-8}$

$\to\sf{x=2y-4...............(i)}$

According to the 2nd condition :-

• 6 years later from now, Ram will be only 1.5 times as old as Shyam.

After 6 years ,

• Age of Ram = (x+6) years
• Age of Shyam = (y+6) years

$\to\sf{x+6=1.5(y+6)}$

$\to\sf{x+6=1.5y+9}$

• Put x = 2y-4 from eq(1).

$\to\sf{2y-4+6=1.5y+9}$

$\to\sf{0.5y=7}$

$\to\sf{y=14}$

• Present age of Shyam = 14 years
• Present age of Ram = 2×14-4 = 24 years.

Answer 2

$\huge\red{Answer}$

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Let Shyam age 5 years back be x, so Ram's age 3x

Their present age is Shyam x + 5 and Ram 3x + 5

The age of Ram will twice the age of Shyam after 10 years.

After 10 years their ages will be

Shyam’s age x + 5 + 10 and Ram's age 3x + 5 + 10

As per statement

3x + 15 = 2 (x + 15)

3x + 15 = 2x + 30

3x - 2x = 30 - 15

x = 15

Thus Shyam's age 5 years earlier was 15 years and Ram's age was 3x = 3 × 15 = 45 years

Their present ages

Shyam’s age 15 + 5 = 20 years

Ram's age 45 + 5 = 50 years

Answer the present ages of Shyam’s is 20 years and Ram's age 50 years

jai siya ram☺ __/\__

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