Question

A and B started simultaneously towards each other form places X and Y, respectively. After meeting at point M on the way, A and B took 3.2 hours and 7.2 hours, to reach Y and X, respectively. Then how much time (in hours) they took to reach at point M?
1. 4.8
2. 5
3. 4
4. 5.2

Answer 1

Correct Answer - Option 1 : 4.8

Given:

A and B are moving towards each other from places X and Y

After meeting at a point M they reach each other's starting point X and Y in 3.2 hours and 7.2 hours.

Formula:

S₁ : S₂ = √(T₂/T₁)

S₁ = Speed of car A

S₂ = Speed of car B

T₁ = Time taken by car A to cover distance

T₂ = Time taken by car B to  cover distance 

Concept:

In relative speed when both object coming to each other their speed becomes sum of their speed. 

Calculation:

Let T be the time taken by them to reach point M.

S₁ : S₂ = √(7.2/3.2) = 3 : 2

Let ratio constant be x

then S₁ = 3x and S₂ = 2x

So, T = {(2x × 7.2) + (3x × 3.2)}/(3x + 2x) hours

⇒ T = (14.4x + 9.6x)/5x hours

⇒ T = 24x/5x = 4.8 hours

∴ The time taken by them to reach point M was 4.8 hours.