Arithmetic

Time, Speed & Distance

Medium

applied

A runs 3 times as fast as B. If A gives B a start of 30 meters, how far must the goal on the race course be so that A and B reach it at the same time?

80 m

42 m

45 m

54 m

✅ Correct Option: 3

Let B's speed be $v$ .

A runs 3 times as fast as B, so A's speed is $3v$ .

Let the goal distance from A's starting point be $d$ meters.

B gets a 30-meter head start, so:

A has to cover: $d$ meters
B has to cover: $(d - 30)$ meters

Since they reach the goal at the same time, their times are equal.

Time taken by A:

$\text{Time} = \dfrac{d}{3v}$

Time taken by B:

$\text{Time} = \dfrac{d - 30}{v}$

Setting the times equal:

$\dfrac{d}{3v} = \dfrac{d - 30}{v}$

$\dfrac{d}{3} = d - 30$

$d = 3(d - 30)$

$d = 3d - 90$

$d - 3d = -90$

$-2d = -90$

$d = 45$

Therefore, the goal must be 45 meters from A's starting point.

2025: 13 May Shift 1

A swimmer whose speed in still water is 6 km/hr, swims between two points in a river and returns to the starting point. He took 20 minutes more to cover the distance upstream than downstream. If the speed of the stream is 3 km/hr, then the distance between the two points is:

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:

2026: 19 May Shift 1

A man rows a boat downstream 30 km and upstream 20 km. It takes him 5 hours to cover each distance. Which of the following are TRUE?

(A) The speed of the boat in still water is 10 km/hr.

(B) The speed of the boat in still water is 5 km/hr.

(D) The speed of the current is 6 km/hr.

Choose the correct answer from the options given below:

2025: 30 May Shift 2

In a 200 m race, Rohan completes the race in 8 seconds and Vivan completes the race in 10 seconds. By how much distance Rohan beats Vivan?

2025: 29 May Shift 2

A man rows a boat such that it covers a distance upstream in twice the time taken by him to cover the same distance downstream. If the speed of stream is 5 km/h, the speed of boat in still water is:

2025: 3 June Shift 1

A man rows 15 km upstream in 5 hours and 25 km downstream in 5 hours each time, then the speed of the stream is

A runs 3 times as fast as B. If A gives B a start of 30 meters, how far must the goal on the race course be so that A and B reach it at the same time?

Solution

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