Arithmetic

Time, Speed & Distance

Medium

applied

'A' can run 1km in 5 minutes 20 seconds and 'B' can run the same distance in 6 minutes. How many meters start can 'A' give 'B' in a kilometer race so that they finish the race together?

14.4 meter

11.1 meter

111.1 meter

144.1 meter

✅ Correct Option: 3

A is faster than B. The goal is to find how much of a head start A should give B so that when A starts running, B is already ahead, and they both cross the finish line at the same time.

Convert times to seconds:

A's time: 5 minutes 20 seconds $= (5 \times 60) + 20 = 320$ seconds

B's time: 6 minutes $= 6 \times 60 = 360$ seconds

For them to finish together, they must take the same time. Since A is faster, A will run the full 1000 meters while B runs less distance (because B started ahead).

In A's time (320 seconds), the distance B can run needs to be calculated.

B's speed $= \dfrac{\text{Distance}}{\text{Time}}$

$= \dfrac{1000}{360}$ m/s

$= \dfrac{25}{9}$ m/s

Distance B covers $= \text{B's speed} \times \text{A's time}$

$= \dfrac{1000}{360} \times 320$

$= \dfrac{1000 \times 320}{360}$

$= \dfrac{320000}{360}$

$= 888.89$ meters

Head start $= \text{Total distance} - \text{Distance B runs}$

$= 1000 - 888.89$

$= 111.11$ meters

Therefore, A can give B a head start of 111.1 meters.

2026: 19 May Shift 2

In a 1000 m race, Arun reaches the final point in 56 seconds and Pradeep reaches in 70 seconds. By how much distance does Arun beat Pradeep?

2025: 15 May Shift 2

A fisherman is rowing a boat. He takes 6 hours to row 48 km upstream whereas he takes 3 hours to go to the same distance downstream.

Based on the above information, which of the following are correct?

(A) His speed of rowing in still water is 10 km/hour.

(B) The speed of the stream is 3 km/hour.

(D) The speed of the stream is 4 km/hour.

Choose the correct answer from the options given below:

2024: 16 May Shift 1

Arun's speed of swimming in still water is $5 \mathrm{~km} / \mathrm{hr}$ . He swims between two points in a river and returns back to the same starting point. He took $20$ minutes more to cover the distance upstream than downstream. If the speed of the stream is $2 \mathrm{~km} / \mathrm{hr}$ , then the distance between the two points is :

2025: 22 May Shift 1

A man rows 24 km upstream in 6 hours and 36 km downstream in 6 hours each time, then the speed of the boat in the still water is

2025: 22 May Shift 1

Two runners A and B complete a 150 meters race in 24 seconds and 36 seconds respectively. By how many meters will A defeat B?

2025: 13 May Shift 2

The speed of a motorboat in still water and that of the current of water is in a ratio of 27:5. The boat goes along the current from point A to point B in 3 hours 40 minutes. How much time will it take to come back from B to A?

'A' can run 1km in 5 minutes 20 seconds and 'B' can run the same distance in 6 minutes. How many meters start can 'A' give 'B' in a kilometer race so that they finish the race together?

Solution

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