Question

Mahesh, Dinesh and Suresh start at the same time in the same direction to run around a circular stadium. Mahesh completes a round in 252 seconds, Dinesh in 308 seconds and Suresh in 198 seconds, all starting at the same point. After what time will they meet again at the starting point?

• A. 28 minutes 16 seconds
• B. 35 minutes
• C. 46 minutes 12 seconds
• D. 52 minutes 30 seconds

Hint:

Whenever a question asks when "bells will ring together" or "runners will meet at the start," always calculate the LCM of the given time periods.

Answer 1

The Correct Option is C

Concept: To find when multiple objects starting together at a circular track will meet again at the starting point, we must calculate the Least Common Multiple (LCM) of the time taken by each individual to complete one full revolution.

Step 1: Prime Factorization of the time intervals.

• $252 = 2^2 \times 3^2 \times 7$
• $308 = 2^2 \times 7 \times 11$
• $198 = 2 \times 3^2 \times 11$

Step 2: Calculating the LCM.
The LCM is the product of the highest powers of all prime factors involved: \[ \text{LCM} = 2^2 \times 3^2 \times 7 \times 11 = 4 \times 9 \times 7 \times 11 = 2772 \text{ seconds.} \]

Step 3: Converting seconds to minutes.
\[ 2772 \div 60 = 46 \text{ minutes and } 12 \text{ seconds.} \]