Arithmetic

Time, Speed & Distance

Medium

Two locations A and B are at diametrically opposite ends of a circular track. Rekha starts running along the track from location A in the clockwise direction. Sajal starts running simultaneously along the track in the anticlockwise direction from location B. If the length of the circular track is 14 km, and the speeds of Rekha and Sajal are in the ratio 5: 2, then the distance, in km, travelled by Rekha, when they meet at location B for the first time, is

✅ Correct Option: 2

$A$ and $B$ are diametrically opposite, so the arc from $A$ to $B$ (either direction) is $\dfrac{14}{2} = 7$ km.

Let speeds be $5v$ (Rekha) and $2v$ (Sajal). They run in opposite directions.

For them to meet at $B$ , both must be at $B$ at the same time $t$ .

Sajal starts at $B$ and moves anticlockwise, so she returns to $B$ after each full lap. Her distances at $B$ are $0, 14, 28, \ldots$ , that is multiples of $14$ .

Rekha starts at $A$ and moves clockwise, reaching $B$ first after $7$ km, then every $14$ km after that. Her distances at $B$ are $7, 21, 35, \ldots$ , i.e. $7 + 14k$ .

Since speeds are in ratio $5 : 2$ , distances covered in the same time are in ratio $5 : 2$ .

If Sajal covers $14m$ km, Rekha covers $\dfrac{5}{2} \cdot 14m = 35m$ km.

Rekha must be at $B$ , so $35m$ must be of the form $7 + 14k$ :

$35m = 7 + 14k$ , i.e. $5m - 2k = 1$

Smallest positive integer solution: $m = 1$ , $k = 2$ .

Rekha's distance $= 35 \times 1 = 35$ km.

Answer $= 35$

IPMAT Indore 2022

When Geeta increases her speed from $12$ km/hr to $20$ km/hr, she takes one hour less than the usual time to cover the distance between her home and office. The distance between her home and office is ___________ km.

IPMAT Indore 2023

A helicopter flies along the sides of a square field of side length 100 kms. The first side is covered at a speed of 100 kmph, and for each subsequent side the speed is increased by 100 kmph till it covers all the sides. The average speed of the helicopter is

IPMAT Indore 2020

Two friends run a 3-kilometer race along a circular course of length 300 meters. If their speeds are in the ratio 3:2, the number of times the winner passes the other is __________.

IPMAT Indore 2022

In a 400-metre race, Ashok beats Bipin and Chandan respectively by 15 seconds and 25 seconds. If Ashok beats Bipin by 150 metres, by how many metres does Bipin beat Chandan in the race?

IPMAT Indore 2019

Two small insects, which are $x$ metres apart, take $u$ minutes to pass each other when they are flying towards each other, and $v$ minutes to meet each other when they are flying in the same direction. Then, the ratio of the speed of the slower insect to that of the faster insect is

IPMAT Indore 2026

A man starts walking from point A to point B at 4 km/hr. After 30 minutes, a woman starts from point A at 6 km/hr. If the woman reaches point B 20 minutes earlier than the man, then the distance between A and B in km is ___

Solution

Related questions:

Keyboard Shortcuts

IPMAT Indore Past Year Questions (Topic-Wise)