Question

A and B started at the same time from X towards Y at the speed of 30 kmph and 50 kmph respectively. If the distance (XY) is 150 km and B after reaching Y starts back towards X immediately, how far from X would A and B meet?
a.120km
b.112.5km
c.125km
d.150km
​

Answer 1

Answer:

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Answer 2

Answer:

From X at  112.5km distance A and B will meet.

Explanation:

• For 'B': The distance between X and Y is  = 150 km

                     Speed = 50 km/hr

       As we know speed = $\frac{Distance}{Time}$  So, Time = $\frac{distance}{speed}$

       To go from X to Y time taken by B =  $\frac{distance}{speed}$ = $\frac{150}{50}$ = 3 hr.

• For 'A': The distance between X and Y is  = 150 km

                     Speed = 30 km/hr

       As we know speed = $\frac{Distance}{Time}$  So, Time = $\frac{distance}{speed}$

       To go from X to Y time taken by A =  $\frac{distance}{speed}$ = $\frac{150}{30}$ = 5 hr.

• In 3 hour B will reach to Y point but A will not.

       In 3 hr the distance covered by A = speed × time = 30 × 3 = 90 km

       Suppose after 't' time when B starts back from Y point, A and B will meet.

       In 't' time distance covered by B = 50 × t = 50t

       In 't' time distance covered by A = 30 × t = 30t

From X point A has covered (90 + 30t) km distance and from Y point B has covered 50t km distance. Both of them have covered a tptal of 150km distance.

  Now we can write, 90 + 30t + 50t = 150

                                   80t = 150 - 90 = 60

                                      t = 60/80 =3/4 hr

∴ The meeting point distance from X = distance covered by A

                                                              = 90 + 30(3/4)

                                                              = 112.5 km.

   

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