A and B can do a piece of work in 20 days and 30 days respectively. If they work

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Question: A and B can do a piece of work in 20 days and 30 days respectively. If they work together for 10 days, how much of the work is left?

Options:

Correct Answer: 1/3

Solution:

A\'s rate = 1/20, B\'s rate = 1/30. Combined rate = 1/20 + 1/30 = 1/12. In 10 days, they complete 10/12 = 5/6 of the work. Remaining = 1 - 5/6 = 1/6.

A and B can do a piece of work in 20 days and 30 days respectively. If they work together for 10 days, how much of the work is left?

A and B can do a piece of work in 20 days and 30 days respectively. If they work together for 10 days, how much of the work is left?

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: Find the combined work rate of A and B when they work together. Add A's rate (1/20) and B's rate (1/30).
Step 4: To add the fractions, find a common denominator. The least common multiple of 20 and 30 is 60. Convert the rates: A's rate becomes 3/60 and B's rate becomes 2/60.
Step 5: Now add the two rates: 3/60 + 2/60 = 5/60. This simplifies to 1/12. So, together they can complete 1/12 of the work in one day.
Step 6: Calculate how much work A and B can complete in 10 days. Multiply their combined rate (1/12) by 10 days: 10 * (1/12) = 10/12, which simplifies to 5/6 of the work.
Step 7: Determine how much work is left after 10 days. Since they completed 5/6 of the work, subtract this from the total work (1): 1 - 5/6 = 1/6.
Step 8: The remaining work after A and B work together for 10 days is 1/6.

Work Rate Calculation – Understanding how to calculate individual work rates and combine them to find the total work done over a period.
Fractional Work Completion – Applying fractions to determine the portion of work completed and the remaining work.