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CAT 2020 Slot 1 — QA Question 3

Basics of TSD/ProportinalityEasy

Leaving home at the same time, Amal reaches 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?

Answer & solution

  • A

    13

  • B

    14

  • C

    11

  • 12

Solution

Easy

The distance is fixed. Two speeds give two travel times whose difference equals the gap between the two arrival times. Solve for the distance, then compute the speed needed for the required 50-minute trip.

1

Translate the arrival-time gap into a time difference. Arriving at 10:15 vs 9:40 means the slower trip takes 3535 minutes =712=\tfrac{7}{12} hour longer. With distance dd km:

d8−d15=3560=712⇒ d⋅15−8120=712⇒ d⋅7120=712⇒ d=10 km\begin{aligned} &\frac{d}{8}-\frac{d}{15}=\frac{35}{60}=\frac{7}{12}\\ &\Rightarrow\ d\cdot\frac{15-8}{120}=\frac{7}{12}\\ &\Rightarrow\ d\cdot\frac{7}{120}=\frac{7}{12}\\ &\Rightarrow\ d=10\ \text{km} \end{aligned}
2

Find the required speed. Leaving 9:10 and reaching 10:00 allows 5050 minutes =56=\tfrac{5}{6} hour for the same 1010 km.

speed=dtime=105/6=10×65=12 km/h\begin{aligned} &\text{speed}=\frac{d}{\text{time}}=\frac{10}{5/6}=10\times\frac{6}{5}=12\ \text{km/h} \end{aligned}
12 km/h12\ \text{km/h}
CAT 2020 Slot 1 QA Q3: Leaving home at the same time, Amal reaches office at 10:15 am if he travels at 8 km/hr, and at 9:40 am if he — Solution | TheCATExam