Question

Choose the correct answer from the alternative given.
A can go round a circular path $8$ times in $40$ minutes. If the diameter of the circle is increased to $10$ times the original diameter, the time required by A to go round the new path once travelling at the same speed as before is:

• A. $25$ min
• B. $20$min
• C. $50$ min
• D. $100$ min

Answer 1

The correct option is C $50$ min

Circumference $=$ $2\pi r$ $=\frac{44}{7}\times r$ metre
Distance covered in $8$ times $=8$ $\times 2\pi r$ = 16$\pi r$ metres.

Speed = $\frac{Distance}{Time}$

= $\frac{16\pi r}{40}metres/minute=\frac{2\pi r}{5}metres/minute$

New circumference $=2$$\pi r\times 10=20\pi r$

Hence, required time $=\frac{20\pi r}{2\pi r}\times 5$ minute $=50$minutes.