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?

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:
$$\frac{280}{60} = \frac{14}{3} = 4 \frac{2}{3}$$​ hours
Final Answer
So the correct answer is (a)