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