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

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.