Quants Questions for CLAT | QB Set 17

A rescue team organised a training exercise on a wide river. Two motorboats, Boat A and Boat B, started from opposite banks and moved towards each other. Boat A travelled at a speed of 30 km/h, while Boat B travelled at 45 km/h. The distance between the two banks was 150 km. At the same time, a drone was launched from Boat A and flew continuously towards Boat B at a speed of 75 km/h. As soon as it reached Boat B, it immediately turned back towards Boat A, repeating this process until the boats finally met.

Meanwhile, another rescue boat, Boat C, started from the same bank as Boat A and moved in the same direction at 24 km/h. After some time, Boat D started from the same point and travelled in the same direction at 36 km/h. The organisers used these movements to teach the concept of relative speed, which helps calculate the time taken by moving objects to meet, overtake, or move apart. Relative speed depends on whether the objects move in the same direction or opposite directions. The exercise provided several practical examples of relative speed calculations.

Questions

Q1. How much time will Boat A and Boat B take to meet?

A. 1.5 hours
B. 2.5 hours
C. 3 hours
D. 2 hours

Q2. What distance will the drone cover before Boat A and Boat B meet?

A. 120 km
B. 135 km
C. 150 km
D. 180 km

Q3. If Boat D starts at the same point as Boat C and both move in the same direction, how much time will Boat D take to gain a lead of 24 km over Boat C?

A. 1 hour
B. 2 hours
C. 3 hours
D. 4 hours

Q4. Two boats are moving in opposite directions at 28 km/h and 32 km/h. If they are 180 km apart, after how many hours will they meet?

A. 3 hours
B. 2 hours
C. 4 hours
D. 5 hours

Q5. A cyclist and a scooter rider move in the same direction at speeds of 18 km/h and 30 km/h respectively. If the cyclist is 24 km ahead, how much time will the scooter rider take to catch up?

A. 2 hours
B. 3 hours
C. 1.5 hours
D. 4 hours

Answers with Detailed Explanation

Q1. Answer: D (2 hours)

When two objects move towards each other:

Relative Speed = Sum of Speeds

= 30 + 45
= 75 km/h

Time taken to meet:

= Distance ÷ Relative Speed

= 150 ÷ 75

= 2 hours

Answer: D

Q2. Answer: C (150 km)

From Q1, the boats meet after 2 hours.

The drone flies continuously at 75 km/h.

Distance covered by drone:

= Speed × Time

= 75 × 2

= 150 km

Answer: C

Q3. Answer: B (2 hours)

Boat C speed = 24 km/h
Boat D speed = 36 km/h

Since both move in the same direction:

Relative Speed = Difference of Speeds

= 36 − 24

= 12 km/h

Boat D must gain 24 km.

Time = Distance ÷ Relative Speed

= 24 ÷ 12

= 2 hours

Answer: B

Q4. Answer: A (3 hours)

Relative speed when moving in opposite directions:

= 28 + 32

= 60 km/h

Time taken:

= 180 ÷ 60

= 3 hours

Answer: A

Q5. Answer: A (2 hours)

Cyclist speed = 18 km/h
Scooter speed = 30 km/h

Relative speed:

= 30 − 18

= 12 km/h

Distance gap = 24 km

Time required:

= 24 ÷ 12

= 2 hours

Answer: A