Question

A man by walking diametrically across a circular grass plot takes 45 seconds less than)f he had kept to the circular path round the outside. He walks 80 metre a minute. What is the diameter of the grass plot. $(\pi =\frac{22}{7})$

• A. 105 cm
• B. 115 cm
• C. 135 cm
• D. 125 cm

Answer 1

The correct option is A 105 cm

Let the diameter of the circle be $d$
Time taken to reach from $A$ to $B$ diametrically be $t$
$\therefore$ Time taken to reach from $A$ to $B$ while on the circular path =$(t+45)s$
This path is semicircular
$\therefore$ To cover a distance of $\frac{\pi d}{2}$ the man takes $(t+45)s$
In $1$ min the man covers=$80m$
$\therefore$ \In $(t+45)s=\frac{80}{1}\times (t+45)$

$=\frac{80}{60}\times (t+45)s$

$\therefore \frac{\pi d}{2}=\frac{80}{60}\times (t+45)s$
Also,
$d=\frac{80}{60}t$
$=>d=\frac{8}{6}t$

$=>t=\frac{6d}{8}$

$\therefore \frac{\pi d}{2}=\frac{80}{60}(\frac{6d}{8}+45)$

$=>\frac{\pi d}{2}=\frac{4}{3}\left(\frac{6d+360}{8}\right)$

$=>d=\frac{7}{22\times 3}(6d+360)$

$=>d=\frac{7d}{11}+38.18$

$=>d=\frac{38.18\times 11}{4}$
$=>d=104.995$
$=>d\simeq 105m$