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The speeds of two brothers P and Q are in the ratio of 6:7.P takes 40 minutes more than Q to reach their home. How long does P take to reach home?
Question

The speeds of two brothers P and Q are in the ratio of 6:7.P takes 40 minutes more than Q to reach their home. How long does P take to reach home?

A.

423 \frac23​ hr

B.

323 \frac23​ hr

C.

413\frac 13​ hr

D.

213\frac 13​ hr

Correct option is A

Given:
Ratio of speeds of P and Q = 6 : 7
Difference in their time = 40 minutes
Formula Used:
For a constant distance, time is inversely proportional to speed.
Solution:
Since the speed ratio is 6 : 7, the time ratio will be the inverse:
Ratio of time of P and Q = 7 : 6
The difference in time in terms of ratio units:
7 units - 6 units = 1 unit
We are given that this difference corresponds to 40 minutes:
1 unit = 40 minutes
Find the time taken by P (which is 7 units):
Time taken by P = 7 × 40 = 280 minutes
Convert the time into hours:
28060=143=423\frac{280}{60} = \frac{14}{3} = 4 \frac{2}{3}​ hours
Final Answer
So the correct answer is (a)

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