Question

The radius of the front wheel and rear wheel of a cycle are 14 cm and 21 cm, respectively. In covering a certain distance the front wheel made 45 revolutions. Find the number of revolutions made by the rear wheel in covering the same distance. ​

Answer 1

Given:

• Radius of front wheel = 14cm
• Radius of rear wheel = 21cm

• To complete a certain distance front wheel revolve 45 times

To Find:

• How many times did the rear wheel revolves to cover the same distance ?

Solution:

${\small{\tt{Circumference \ of \ front \ wheel }}}\\ {\small{\tt{= 2 \pi r = 2 × \dfrac{22}{7} × 14 = 88cm}}}$

Let it covers ‘x’ cm distance in 45 revolutions

Then ,

${\small{\tt{ \implies{x \: = (45 × 88)cm = 3960 cm }}}}$

${\small{\bold{\therefore Distance = 3960 cm}}}$

${\small{\tt{Circumference \ of \ rear \ wheel }}}\\ {\small{\tt{= 2 \pi r = 2 × \dfrac{22}{7} × 21= 132cm}}}$

${\small{\tt{No. \ of \ revolutions \ made \ by \ rear \ wheel = \dfrac{Distance}{Circumference}}}}$

${\small{\tt{ \longrightarrow{No. \ of \ revolutions \ made \ by \ rear \ wheel = \dfrac{3960}{132}}}}}$

${ \red{\small{\tt{ \longrightarrow{No. \ of \ revolutions \ made \ by \ rear \ wheel = 30}}}}}$