Question

Stations X and Y are 180 km distance away. Two trains P and Q start simultaneously from X at speeds 15 km/h and 10 km/h to reach Y while returning from Y to the transmeton
Z Find the distance travelled by Q when both trains meet. (Assume that both trains are returning immediately from Y)
36 kms
132 kms
150 km
144 kms​

Answer 1

Given :- Stations X and Y are 180 km distance away. Two trains P and Q start simultaneously from X at speeds 15 km/h and 10 km/h to reach Y while returning from Y to the transmeton Z Find the distance travelled by Q when both trains meet. (Assume that both trains are returning immediately from Y)

36 kms

132 kms

150 km

144 kms

Solution :-

→ Total distance from station X and Y = 180km.

→ Speed of P = 15km/h.

So,

→ Time taken by P to reach Y = Distance/speed = 180/15 = 12 hours.

Similarly,

→ speed of Y = 10km/h.

→ Time taken by Q to reach Y = Distance/speed = 180/10 = 18 hours.

Now, after reaching to Y, P return immediately .

As, we can see , train P reached at Y 6 hours before, and return for Z in middle of X and Y .

So,

→ in 12 hours Q covered distance = 12 * 10 = 120 km .

Than,

→ distance left to be covered by Q = 180 - 120 = 60 km.

we can say that, now distance b/w P and Q is 60km. and Both are in Opposite direction .

Than,

→ usual speed of both = (15 + 10) = 25 km/h. (Opposite direction) .

Therefore,

→ Time taken by them to meet at Z now = distance between them / usual speed = 60/25 = 2.4 hours.

Hence,

→ in 2.4 hours Q cover distance = 2.4 * 10 = 24 km.

Thus,

→ Total distance covered by Q to reach Z = 120 + 24 = 144 km.(Ans.)

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