CAT 2020 Slot 1 QA Question & Solution
ArithmeticEasy
Question
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?
Options
13
12
14
11
Solution
The difference in the time take to traverse the same distance $'d'$ at two different speeds is 35 minutes. Equating this: $\frac{d}{8}-\frac{d}{15}\ =\ \frac{35}{60}$
On solving, we obtain $d = 10 kms$. Let $x kmph$ be the speed at which Amal needs to travel to reach the office in 50 minutes; then
$\frac{10}{x}=\frac{50}{60}\ or\ x\ =\ 12\ kmph$.
Hence, Option B is the correct answer.