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  1. P and Q are two cities. A boy travels on cycle from P to Q at a speed of 20 km per hr. and returns at the rate of 10 km per hr. Find his average speed for the whole journey.
    1. 13
      2
      kmph
      3
    2. 12
      1
      kmph
      3
    3. 13
      1
      kmph
      3
    4. 12
      2
      kmph
      3
Correct Option: C

Let the speed between P and Q be x km.

Then time taken to cover x km. P to Q =
x
hrs.
20

Time taken to cover x km from Q to P at 10 km per hr. P to Q
=
x
hrs.
10

∴  Total distance covered
= x + x = 2x km.
Time taken to cover 2x km.
=
x
+
x
=
x + 2x
=
3x
hrs.
20102020

∴ Average Speed =
2x
=
2x × 20
3x/203x

=
40
km per hr.
3

= 13
1
km per hr.
3


Second Method : Here, x = 20 km per hr.
y = 10 km per hr
∴ Average Speed [∵  Distance is same]
=
2xy
=
2 × 20 × 10
x + y20 + 10

=
400
=
40
= 13
1
km per hr.
3033


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