# Quantitative Aptitude -Time,Speed and Distance-Game or Race question-3!

PSA_LEVEL-UP_QNR37. At a game of billiards, Amar can give Chanu 20 in 60 and Amar can give Bhanu 15 points in 60. How many points can Bhanu give Chanu in a game of 90?

a) 20

b) 30

c) 40

d) 10

Ans:

First of all we would like to understand what the sentence “Amar can give Chanu 20 in 60” means!

The above sentence means that:
(i) Amar is a better/efficient player than Chanu and
(ii) if Amar gives Chanu 20 points at the start and he himself starts with zero, both of them will finish the game of 60 points at the same time.

You can actually convert these two into another set of sentences that should read as if this game were not billiards but a race. Below are the set of statements:
(i) Amar is a faster runner than Chanu and
(ii) if Amar gives Chanu 20 metres of lead at the start of race of 60 metres, both of them will finish at the same time.

Since time is same, distance travelled will be in the same ratio as speed.
Let speeds of Amar, Bhanu and Chanu be Sa, Sb and Sc units.

As per the given conditions in the question,

Sa/Sc=60/(60-20) = 60/40
Sa/Sb = 60/(60-15) = 60/45

Thus, Sb/Sc=45/40
Since we need to create a game out of 90, we multiply and divide by 2.
=> Sb/Sc=(45*2)/(40*2) = 90/80

From the ratio 90:80 we see that Bhanu can give Chanu a lead of (90-80) or 10 metres in a race of 90 metres. Option d.

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