Time, Speed and Distance Question 8 - CAT 2020
Leaving home at the same time, Amal reaches the office at 10:15 am if he travels at 8 km/hr, and at 9:40 am if he travels at 15 km/hr. Leaving home at 9:10 am, at what speed, in km/hr, must he travel so as to reach office exactly at 10 am?
Step-by-Step Explanation
Find the distance (d) to the office:
The time difference between arriving at 10:15 am and 9:40 am is 35 minutes (35/60 hours).
d/8 − d/15 = 35/60
(15d − 8d)/120 = 7/12
7d/120 = 7/12 ⟹ d = 10 km
Calculate the required speed for the 10:00 am target:
Amal leaves home at 9:10 am and wants to arrive exactly at 10:00 am.
Available Time = 50 minutes = 50/60 = 5/6 hour
Required Speed = 10/(5/6) = 10 × 6/5 = 12 km/hr
Correct Option: B
💡 FundaMakers Tip:
Use the product-over-difference formula for late/early arrival problems over a constant distance:
D = [S₁ × S₂/|S₁ − S₂|] × Δt
Here,
D = [8 × 15/(15 − 8)] × 35/60
= 120/7 × 7/12 = 10 km
This formula bypasses separate fractional equations and gives you the total distance in a single step.