If A, B and C do a piece of work in 10, 15 and 18 days, respectively. Find the ratio of work done by them in a day.a)5 : 6 : 9b)6 : 5 : 9c)10 : 15 : 18d)9 : 6 : 5Correct answer is option 'D'. Can you explain this answer?

Question

Answer

Understanding the Problem
In this problem, we need to determine the ratio of work done by A, B, and C in a day based on the time each of them takes to complete a piece of work.
Work Done in One Day
- A's Work Rate: A can complete the work in 10 days. Therefore, A's work done in one day is 1/10 of the work.
- B's Work Rate: B can complete the work in 15 days. Therefore, B's work done in one day is 1/15 of the work.
- C's Work Rate: C can complete the work in 18 days. Therefore, C's work done in one day is 1/18 of the work.
Finding the Common Denominator
To compare their work rates, we should find a common denominator for the fractions:
- The least common multiple (LCM) of 10, 15, and 18 is 90.
Now, we can express each person's work rate in terms of the common denominator:
- A's Work: (1/10) = 9/90
- B's Work: (1/15) = 6/90
- C's Work: (1/18) = 5/90
Calculating the Ratio
Now we can establish the work done by A, B, and C in a day as follows:
- A's Work Done: 9 parts
- B's Work Done: 6 parts
- C's Work Done: 5 parts
The ratio of work done by A, B, and C is:
- Ratio: 9 : 6 : 5
Conclusion
Thus, the correct answer is option 'D': 9 : 6 : 5. This ratio clearly illustrates the amount of work each person contributes in one day relative to each other.

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