**Question:**

The diameters of the front and rear wheels of a tractor are 80 cm and 2 m respectively. Find the number of revolutions that a rear wheel makes to cover the distance which the front wheel covers is 800 revolutions.

**Solution:**

Radius of the front wheel $=40 \mathrm{~cm}=\frac{2}{5} \mathrm{~m}$

Circumference of the front wheel $=\left(2 \pi \times \frac{2}{5}\right) \mathrm{m}=\frac{4 \pi}{5} \mathrm{~m}$

Distance covered by the front wheel in 800 revolutions $=\left(\frac{4 \pi}{5} \times 800\right) \mathrm{m}=(640 \pi) \mathrm{m}$

Radius of the rear wheel = 1 m

Circumference of the rear wheel $=(2 \pi \times 1)=2 \pi \mathrm{m}$

$\therefore$ Required number of revolutions $=\frac{\text { Distance covered by the front wheel in } 800 \text { revolutions }}{\text { Circumference of the rear wheel }}$

$=\frac{640 \pi}{2 \pi}$

$=320$

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