A can do a work in 40 days, B in 60 days, and C in 120 days. If they work togeth

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Question: A can do a work in 40 days, B in 60 days, and C in 120 days. If they work together for 10 days, how much of the work is completed?

Options:

Correct Answer: 1/4

Solution:

Combined rate = (1/40 + 1/60 + 1/120) = 1/24. In 10 days, they complete 10/24 = 5/12 of the work.

A can do a work in 40 days, B in 60 days, and C in 120 days. If they work together for 10 days, how much of the work is completed?

A can do a work in 40 days, B in 60 days, and C in 120 days. If they work together for 10 days, how much of the work is completed?

Step 1: Determine the work rate of each person. A can complete the work in 40 days, so A's rate is 1/40 of the work per day.
Step 2: B can complete the work in 60 days, so B's rate is 1/60 of the work per day.
Step 3: C can complete the work in 120 days, so C's rate is 1/120 of the work per day.
Step 4: Add the rates of A, B, and C together to find their combined work rate: 1/40 + 1/60 + 1/120.
Step 5: To add these fractions, find a common denominator. The least common multiple of 40, 60, and 120 is 120.
Step 6: Convert each rate to have the common denominator of 120: A's rate becomes 3/120, B's rate becomes 2/120, and C's rate becomes 1/120.
Step 7: Now add the rates: 3/120 + 2/120 + 1/120 = 6/120.
Step 8: Simplify 6/120 to 1/20. This means together they can complete 1/20 of the work in one day.
Step 9: To find out how much work they complete in 10 days, multiply their combined rate by 10: 10 * (1/20) = 10/20.
Step 10: Simplify 10/20 to 1/2. Therefore, they complete 1/2 of the work in 10 days.

Work Rate Calculation – Understanding how to calculate the combined work rate of multiple workers and how to apply it over a period of time.
Fraction Addition – Adding fractions with different denominators to find a common work rate.
Time and Work Relationship – Applying the relationship between time, work, and rate to determine the portion of work completed.