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Tours for Qutab Minar, Red Fort and Indi...

Tours for Qutab Minar, Red Fort and India Gate start from a tourist agency at `10:00`a.m. Tours for Qutab Minar leave every `10` minutes, tours for Red Fort leave every `15` minutes and tours for India Gate leave every `30` minutes. At what time will the three tours leave from the agency at the same time again?

A

`09:30` a.m

B

`11:30` a.m

C

`10:30` a.m

D

`10:45` a.m

Text Solution

AI Generated Solution

The correct Answer is:
To find out when the tours for Qutab Minar, Red Fort, and India Gate will leave from the agency at the same time again after their initial departure at 10:00 a.m., we need to determine the least common multiple (LCM) of their departure intervals. ### Step-by-Step Solution: 1. **Identify the time intervals:** - Qutab Minar: Every 10 minutes - Red Fort: Every 15 minutes - India Gate: Every 30 minutes 2. **List the time intervals:** - We have the intervals: 10, 15, and 30 minutes. 3. **Find the LCM of the intervals:** - We can use the prime factorization method or the common division method to find the LCM. Here, we'll use the common division method: - Start with the numbers: 10, 15, 30. - Divide by the smallest prime number that can divide at least one of the numbers: - Divide by 2: - 10 ÷ 2 = 5 - 15 remains 15 - 30 ÷ 2 = 15 - Now we have: 5, 15, 15. - Next, divide by 3: - 5 remains 5 - 15 ÷ 3 = 5 - 15 ÷ 3 = 5 - Now we have: 5, 5, 5. - Finally, divide by 5: - 5 ÷ 5 = 1 - 5 ÷ 5 = 1 - 5 ÷ 5 = 1 - Now we have: 1, 1, 1. 4. **Calculate the LCM:** - The LCM is found by multiplying the divisors used: - LCM = 2 × 3 × 5 = 30. 5. **Determine the next time they leave together:** - Since they all leave together at 10:00 a.m., we add the LCM (30 minutes) to this time. - 10:00 a.m. + 30 minutes = 10:30 a.m. ### Final Answer: The three tours will leave from the agency at the same time again at **10:30 a.m.**
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