Distance and Time

 UPSC Prelims 2022--> Q) X and Y run in a 3 Km race along a circular course of length 300 m . there speeds are in the ratio 3:2 if they start together in the same direction, how many times would the first one pass the other (The start of not counted as passing)?

^{Solution :-} 

                   ^X⁄_Y  =  ³⁄₂

_{Lets assume speed Speed of X is 3 m/s}

Then speed of Y =  2 m/s

_{Now Total Rounds =} ³⁰⁰⁰⁄₃₀₀ = 10 Rounds

_{Time taken by X to complete 1 round =} ³⁰⁰⁄₃ = 10 Seconds

_{Time taken by Y to complete 1 round =} ³⁰⁰⁄₂ = 15 Seconds

Round            X            Y

1                    10            15

2                    20            30

3                    30            45

4                    40            60

5                    50            75

6                    60            90

7                    70            105

8                    80            120

9                    90            135

10                  100          150

They will cross each other 3 times

UPSC Prelims 2022--> Q) Two friends X and Y Start running and they run together for 50m in the same direction and reach a point. X turns Right and Runs 60m while Y turns left and runs 40m. Then X turns left and runs 50m and stops , while Y turns right and runs 50m and then stops. How far are the tow friends from each other now?

Solution :- 

Distance Between X and Y = 60m + 40m = 100 m