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CAT 2020 Slot 3 — QA Question 14

Circular RaceEasy

Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, and going in the clockwise direction. If they run at speeds of 15km/hr, 10 km/hr, and 8 km/hr, respectively, how much distance in km will Ravi have run when Anil and Sunil meet again for the first time at the starting point?

Answer & solution

  • A

    4.6

  • B

    4.2

  • C

    5.2

  • 4.8

Solution

Easy

Anil and Sunil meet again "at the starting point" when each has completed a whole number of laps, i.e. after the LCM of their individual lap times. Find that time, then compute the distance Ravi covers in it.

1

Lap times of Anil and Sunil. Track length =3=3 km.

tAnil=315 hr=12 mintSunil=310 hr=18 min\begin{aligned} &t_{\text{Anil}}=\frac{3}{15}\,\text{hr}=12\ \text{min}\\ &t_{\text{Sunil}}=\frac{3}{10}\,\text{hr}=18\ \text{min} \end{aligned}
2

First common return to the start. This is the LCM of the lap times.

T=lcm⁡(12,18)=36 min=0.6 hr\begin{aligned} &T=\operatorname{lcm}(12,18)=36\ \text{min}=0.6\ \text{hr} \end{aligned}
3

Distance run by Ravi in that time. Ravi's speed is 88 km/hr.

dRavi=8×0.6=4.8 km\begin{aligned} &d_{\text{Ravi}}=8\times 0.6=4.8\ \text{km} \end{aligned}
dRavi=4.8 kmd_{\text{Ravi}}=4.8\ \text{km}
CAT 2020 Slot 3 QA Q14: Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, — Solution | TheCATExam