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CAT 1998 — QA Question 15

LCM & HCFEasy
Passage / Data

Answer the next 2 questions based on the following information.

A cow is tethered at point A by a rope. Neither the rope nor the cow is allowed to enter ΔABC.

∠BAC = 30°
I(AB) = I(AC) = 10 m

Three wheels can complete 60, 36 and 24 revolutions per minute. 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?

Answer & solution

  • A

    52s

  • B

    53s

  • 5 s 

  • D

    7.5 s

Solution

The time taken by the white spots on all three wheels to simultaneously touch the ground again will be equal to the LCM of the times taken by the three wheels to complete one revolution.
The first wheel complete 60 revolutions per minute.

This means that to complete one revolution, it takes (6060) = 1 s.

Similarly, the second wheel takes (6036)=53 s to complete one revolution.

Similarly, the third wheel takes 6024=52 s to complete one revolution.

Hence, LCM of 1, 53,52=L.C.M. (1,5,5)H.C.F. (1,3,2)=51=5 s

Hence, option (c).

CAT 1998 QA Q15: Three wheels can complete 60, 36 and 24 revolutions per minute. There is a red spot on each wheel that touches — Solution | TheCATExam