## How to Approach the Tricky questions in Time and Distance Explained by Mr.Gopalakrishnan sir

Q. Two persons A and B started walking from two places P and Q respectively towards Q and P at 8.20 A.M. Their speeds of walking were in the ratio 4:5. They met at a place between P and Q ,spent some time together for coffee and then both started towards their respective destinations at 9.27 A.M. If A reached Q at 10.32 A.M., how much time they spent together?

Options:

a) 17 Minutes b) 15 Minutes C) 10 Minutes d) 22 Minutes e) 25 Minutes

As the problem is silent on the distance covered either by A or by B, the ratio of the time taken by them will be helpful in quickly solving it. As speed and time are inversely proportional, the ratio of time taken by A and B is 5:4.

How much time did A take to cover the distance between P and Q as per the Question? Let the point at which they met be R. A covers the distance between P and R in (9.27 Hours – 8.20 Hours) i.e. in 67 minutes including the time spent together by them at R. A specific point to remember here is that the difference in time should not be computed by simply subtracting the fractions, but by converting the time elements into minutes.( one Hour= 60 Minutes). The actual time taken by him to cover the distance between R and Q is (10.32 Hours-9.27 Hours) i.e. 65 Minutes. The total time taken by A to cover the distance between P and Q = Time taken to cover the distance between P and R + The time spent with B for coffee + Time taken to cover the distance between R and Q. Let the time (in minutes) they spent together be t. For computing the speed at which A traveled  the resting time (the  time taken for coffee) should not be included. Thus in relation to speed, the actual time taken by A to cover the entire distance between P and Q is 67 Minutes-t Minutes + 65 Minutes. While A takes ( 67-t) and 65 Minutes as actual traveling time, B takes  only (67 -t) X 5/4 Minutes (from Q to R) plus  65X 5/4 Minutes(from R to Q) to complete his journey from Q to P.  While A takes 65 Minutes to cover the distance between R and P, Q takes 65 X 4/5 Minutes to complete the remaining distance between R and Q.

It is therefore clear that :

67-t (Minutes) = 65 X 4/5 (Minutes) = 52 Minutes.

Solving the simple equation, t = 15 Minutes.

The solution is that of finding the time spent together by them which is t.

Answer: b) 15 Minutes.

Illustration:

A

67-t Minutes              (Time taken)                     65 Minutes

P –———————––————- R –——-–———————— Q

52 Minutes (Time taken) 41 Minutes +36 Seconds B

Ratio of their time (A:B) = 52+ 65 Minutes : 52 +(41 Minutes + 36 Seconds).

i.e 117 Minutes : 93 Minutes plus 36 Seconds.

7020 SecondS : 5616 Seconds.

5 : 4

Which is given.

Hence, confirmation of the answer.