Question

Two years ago ram was thrice as old as rahim and 6 years later ram will be 4 years older than twice the age of rahim

Answer 1

Solution :-

Let the present ages of Ram and Rahim be x years and y years respectively.

Case I : Two years ago Ram was thrice as old as Rahim.

=> x - 2 = 3(y - 2)

=> x - 2 = 3y - 6

=> x = 3y - 4 ______(i)

Case II : 6 years later Ram will be 4 years older than twice the age of Rahim.

=> x + 6 = 2(y + 6) + 4

=> x + 6 = 2y + 12 + 4

=> 3y - 4 + 6 = 2y + 12 + 4 [from equation (i)]

=> 3y - 2y = 12 - 6 + 4 + 4

=> y = 14

Putting the value of y in equation (i) we get,

=> x = 3 × 14 - 4

=> x = 42 - 4 = 38

Hence,

The present ages of Ram and Rahim are 38 years and 14 years respectively.

Answer 2

$\huge \underline \mathfrak {Solution:-}$

Let the present age of Ram is X and Rahim is y.

Before 2 years,

Ram's age = x - 2

Rahim's age = y - 2

According to question,

x - 2 = 3( y - 2)

x - 2 = 3y - 6

x = 3y -4 ....(1)

After 6 years,

Ram age = X + 6

Rahim age = y + 6

According to question,

X + 6 = 2( y + 6 ) + 4

X + 6 = 2y + 12 + 4

X = 2y + 10 ....(2)

On comparing eq (1) and (2)

3y - 4 = 2y + 10

3y - 2y = 10 + 4

y = 14

from eq (2)

x = 2 × 14 + 10 = 38

So, present age of Ram is 14 years and Rahim is 38 years.