21 thoughts on “Singles – 3

    • Note that from Q to B the train is losing 27 min by going at 5/6th of speed. So normal time is 135 and new time 162. So 135 min at normal speed of 72 (or 162 min at new speed of 60) gives 162 km.


  1. Sir,
    In the first case it was travelling 5/6 of the speed so time will be 6 / 5 of the time, also 10 min more in the first case. So 60 min should be the time for the first case for 60 km . Why have you considered 50 min ?

  2. Thanks sir, got it. Please post some questions on topics like
    A beats B by 20 min in 100 m race. How much start should A give to C in a 100m race so that both of them reach winning post at the same time?

  3. sir, I understood the way we got 60 and 72kmph but, in this problem, normal speed of the car should be ‘s’ and not ‘5s/6’ right? so ‘s’ came out to be 72 from second case, so normal speed should be 72 and not 60, isn’t it?

  4. but time taken is 6/5x if x is T here.. or if x=time and 5/6 is speed then speed * time = distance and not the time (27 in the equation)

    • Ok,..normal speed is the faster speed, the other is the slower speed. I leave it to you to figure out which takes more time. If you want to insist the slower speed also takes a smaller time then I can’t help you.


  5. i didn’t say slower speed is taking less time, when I say 6/5T – T = 27, that means T here is normal time which came out to be 135 min, and we took 27 min more for slower speed which gives me 162min.. whats wrong in it?

    • I am not getting how what you are saying is different in any way from the answer I have given? I am also saying normal speed is the faster and hence normal time is less i.e. 135. The only difference is which value you have taken as x and which one I have taken as x.

      If we are told my age is ten less than your age and I solve it by taking my age as x and yours as x + 10, and you solve it by taking yours as x and mine as x – 10, the two ages we get will be the same in both cases. But the value of x will obviously not be because we took different things as x.


  6. Sir is this how you did it for the distance from Q to B?

    Speed 5:6
    Time 6:5

    A gap of 1~27, so it would be 27*6=162 and 5*27= 135

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