Arithmetic

Time, Speed & Distance

Medium

applied

In a 10 km race, A, B and C each run at uniform speed, get the first, second and third position respectively. If A beats B by 1 km and B beats C by 1 km, then, by how much distance A beat C?

2 km

1.9 km

1.8 km

2.1 km

✅ Correct Option: 2

When A finishes the 10 km race, B has completed 9 km (A beats B by 1 km).

When B finishes the 10 km race, C has completed 9 km (B beats C by 1 km).

Since they run at uniform speeds, the speed ratio equals the distance ratio when time is the same.

When A completes 10 km, B completes 9 km in the same time.

Speed ratio of A to B:

$A : B = 10 : 9$

When B completes 10 km, C completes 9 km in the same time.

Speed ratio of B to C:

$B : C = 10 : 9$

To combine the ratios $A : B = 10 : 9$ and $B : C = 10 : 9$ :

$A : B : C = 100 : 90 : 81$

When A covers 100 units, C covers 81 units.

When A covers 10 km, C covers:

$\dfrac{81}{100} \times 10 = 8.1$ km

Distance by which A beats C:

$10 - 8.1 = 1.9$ km

Therefore, A beats C by 1.9 km.

2026: 25 May Shift 1

A boat goes downstream at a speed of 18 km/hr and upstream at a speed of 'm' km/hr. The boat travelled 90 km downstream in a river and then returned back taking altogether 12.5 hours. Then which of the following are true ?

A. $m = 12$

B. $m = 15$

C. Speed of water current is 3 km/hr

D. Speed of water current is 1.5 km/hr

Choose the correct answer from the options given below:

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:

2026: 30 May Shift 2

A motorboat completes a round trip of 150 km between two places A and B in 8 hours. If downstream speed of the motorboat is 25 km/hr, then the upstream speed of the motorboat is

2025: 14 May Shift 1

A person can row a boat in still water at the rate of 5 km/hr. It takes him 4 times as long to row upstream of a river as to row downstream to cover same distance in the same river. The speed of flow of the stream is

2026: 18 May Shift 2

Mr. X runs 5 times as fast as Mr. Y. If Mr. X gives Mr. Y a start of 80 meters, how far must the goal on the race course be so that Mr. X and Mr. Y reach it at the same time?

2025: 29 May Shift 2

In a 500 metres race, the ratio of speeds of two participants Meena and Kamal is 4:5 respectively. If Meena has a start of 200 metres, find the distance by which Meena wins.

In a 10 km race, A, B and C each run at uniform speed, get the first, second and third position respectively. If A beats B by 1 km and B beats C by 1 km, then, by how much distance A beat C?

Solution

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