A can do a work in 12 days, B can do it in 18 days, and C can do it in 24 days.

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What’s inside this PDF?

Question: A can do a work in 12 days, B can do it in 18 days, and C can do it in 24 days. If they work together, how long will they take to complete the work?

Options:

Correct Answer: 6

Solution:

A\'s rate = 1/12, B\'s rate = 1/18, C\'s rate = 1/24. Combined rate = 1/12 + 1/18 + 1/24 = 1/4. They will complete the work in 4 days.

A can do a work in 12 days, B can do it in 18 days, and C can do it in 24 days.

Practice Questions

A can do a work in 12 days, B can do it in 18 days, and C can do it in 24 days. If they work together, how long will they take to complete the work?

Questions & Step-by-Step Solutions

A can do a work in 12 days, B can do it in 18 days, and C can do it in 24 days. If they work together, how long will they 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 12 days, so A's rate is 1/12 of the work per day.
Step 3: Calculate B's work rate: B can complete the work in 18 days, so B's rate is 1/18 of the work per day.
Step 4: Calculate C's work rate: C can complete the work in 24 days, so C's rate is 1/24 of the work per day.
Step 5: Add the rates of A, B, and C together to find their combined work rate: 1/12 + 1/18 + 1/24.
Step 6: To add the fractions, find a common denominator. The least common multiple of 12, 18, and 24 is 72.
Step 7: Convert each fraction to have the common denominator of 72: A's rate becomes 6/72, B's rate becomes 4/72, and C's rate becomes 3/72.
Step 8: Add the converted rates: 6/72 + 4/72 + 3/72 = 13/72.
Step 9: The combined rate of A, B, and C is 13/72 of the work per day.
Step 10: To find out how many days it takes to complete the work together, take the reciprocal of the combined rate: 72/13 days.
Step 11: Simplify 72/13 to get approximately 5.54 days, which means they will complete the work in about 5.54 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 Problem – Applying the concept of work done over time to determine how long it will take to complete a task when multiple people are working together.

A can do a work in 12 days, B can do it in 18 days, and C can do it in 24 days.

What’s inside this PDF?

A can do a work in 12 days, B can do it in 18 days, and C can do it in 24 days.

Practice Questions

Questions & Step-by-Step Solutions

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