Three wheels can complete 60, 36, 24 revolutions per minute, respectively. There is a red spot on each wheel that touches the ground at time zero. After how much time all these spots will simultaneously touch the ground again?

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

\frac{5}{2} \sec

\frac{5}{3} \sec

6 \sec

7.5 \sec

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given,
Revolution per minute of first wheel = 60
Revolution per minute of second wheel = 36
Revolution per minute of third wheel = 24
Now, time needed to complete one resolution
First wheel

t_{1} = \frac{60}{60} = 1 \sec

(since 1 min= 60 second)
For, second wheel

t_{2} = \frac{36}{60} s = \frac{3}{5} \sec

For third wheel

t_{3} = \frac{24}{60} = \frac{2}{5} \sec

Now, the time at which the spot of all touch the ground at same time =

LCM of (\frac{1}{1}, \frac{3}{5}, \frac{2}{5})

= \frac{LCM of 1, 3, 2}{HCF  of 1, 5, 5}

= \frac{6}{1}

= 6 \sec

Hence, required time is 6 seconds.
Correct option is 3.

Watch 3-min video & get full concept clarity

tricks from toppers of Infinity Learn

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET