A can do a work in 15 days, B can do it in 20 days, and C can do it in 30 days.

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What’s inside this PDF?

Question: A can do a work in 15 days, B can do it in 20 days, and C can do it in 30 days. If all three work together, how long will it take to complete the work?

Options:

Correct Answer: 6

Solution:

A\'s rate = 1/15, B\'s rate = 1/20, C\'s rate = 1/30. Combined rate = 1/15 + 1/20 + 1/30 = 1/6. They will complete the work in 6 days.

A can do a work in 15 days, B can do it in 20 days, and C can do it in 30 days.

Practice Questions

A can do a work in 15 days, B can do it in 20 days, and C can do it in 30 days. If all three work together, how long will it take to complete the work?

Questions & Step-by-Step Solutions

A can do a work in 15 days, B can do it in 20 days, and C can do it in 30 days. If all three work together, how long will it take to complete the work?

Step 1: Determine how much work A, B, and C can do in one day.
Step 2: Calculate A's work rate: A can complete the work in 15 days, so A's rate is 1/15 of the work per day.
Step 3: Calculate B's work rate: B can complete the work in 20 days, so B's rate is 1/20 of the work per day.
Step 4: Calculate C's work rate: C can complete the work in 30 days, so C's rate is 1/30 of the work per day.
Step 5: Add the work rates of A, B, and C together to find their combined work rate: 1/15 + 1/20 + 1/30.
Step 6: Find a common denominator to add the fractions. The common denominator for 15, 20, and 30 is 60.
Step 7: Convert each fraction: 1/15 = 4/60, 1/20 = 3/60, 1/30 = 2/60.
Step 8: Add the converted fractions: 4/60 + 3/60 + 2/60 = 9/60.
Step 9: Simplify the combined rate: 9/60 can be simplified to 3/20.
Step 10: The combined rate of A, B, and C is 3/20, meaning together they complete 3/20 of the work in one day.
Step 11: To find out how many days it takes to complete the entire work, take the reciprocal of the combined rate: 20/3 days.
Step 12: Calculate 20/3 days, which is approximately 6.67 days.

Work Rate Calculation – Understanding how to calculate individual work rates and combine them to find the total work rate when multiple workers are involved.
Fraction Addition – Adding fractions with different denominators to find a common work rate.
Time and Work Relationship – Applying the relationship between work rate and time to determine how long a task will take when multiple people are working together.

A can do a work in 15 days, B can do it in 20 days, and C can do it in 30 days.

What’s inside this PDF?

A can do a work in 15 days, B can do it in 20 days, and C can do it in 30 days.

Practice Questions

Questions & Step-by-Step Solutions

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