A can do a work in 20 days, B can do it in 30 days, and C can do it in 60 days.

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What’s inside this PDF?

Question: A can do a work in 20 days, B can do it in 30 days, and C can do it in 60 days. If all three work together, how long will they take to complete the work?

Options:

Correct Answer: 5

Solution:

A\'s rate = 1/20, B\'s rate = 1/30, C\'s rate = 1/60. Combined rate = 1/20 + 1/30 + 1/60 = 1/10. They will complete the work in 10 days.

A can do a work in 20 days, B can do it in 30 days, and C can do it in 60 days.

Practice Questions

A can do a work in 20 days, B can do it in 30 days, and C can do it in 60 days. If all three work together, how long will they take to complete the work?

Questions & Step-by-Step Solutions

A can do a work in 20 days, B can do it in 30 days, and C can do it in 60 days. If all three work together, how long will they take to complete the work?

Step 1: Determine how much work A can do in one day. A can complete the work in 20 days, so A's rate is 1/20 of the work per day.
Step 2: Determine how much work B can do in one day. B can complete the work in 30 days, so B's rate is 1/30 of the work per day.
Step 3: Determine how much work C can do in one day. C can complete the work in 60 days, so C's rate is 1/60 of the work per day.
Step 4: Add the rates of A, B, and C together to find their combined work rate. This is 1/20 + 1/30 + 1/60.
Step 5: To add the fractions, find a common denominator. The least common multiple of 20, 30, and 60 is 60.
Step 6: Convert each rate to have the common denominator of 60: A's rate becomes 3/60, B's rate becomes 2/60, and C's rate remains 1/60.
Step 7: Now add the converted rates: 3/60 + 2/60 + 1/60 = 6/60.
Step 8: Simplify the combined rate: 6/60 simplifies to 1/10.
Step 9: The combined rate of 1/10 means that together, A, B, and C can complete 1/10 of the work in one day.
Step 10: To find out how many days it will take to complete the entire work, take the reciprocal of the combined rate: 1 / (1/10) = 10 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 20 days, B can do it in 30 days, and C can do it in 60 days.

What’s inside this PDF?

A can do a work in 20 days, B can do it in 30 days, and C can do it in 60 days.

Practice Questions

Questions & Step-by-Step Solutions

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