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A boy walks from his home to school at 6 kmph. He walks back at 2 kmph. His average speed, in kmph is
(A) 3; (B) 4; (C) 5; (D) $$\sqrt {12}$$;

Discussion:

Suppose the distance from home to school is t km.
Time taken for home to school journey: $$\frac {t}{6}$$
Time taken for school to home journey: $$\frac {t}{2}$$

Hence average speed = $$\frac {distance}{time} = \frac {2t}{\frac{t}{6} + \frac{t}{2}} = 3$$

There fore average speed is 3 kmph.

Note that it is the harmonic mean of the two given speeds instead of arithmetic mean.

## Chatuspathi:

• What is this topic: Elementary Arithmetic
• What are some of the associated concepst: Harmonic Mean
• Where can learn these topics: Cheenta I.S.I. & C.M.I. course, discusses these topics in the ‘Number Theory’ module.
• Book Suggestion: Arithmetic by K.C. Nag