A can complete a work in 8 days, B can complete it in 12 days. If they work toge

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Question: A can complete a work in 8 days, B can complete it in 12 days. If they work together for 4 days, how much work is left?

Options:

Correct Answer: 1/4

Solution:

A\'s rate = 1/8, B\'s rate = 1/12. Combined rate = 1/8 + 1/12 = 5/24. In 4 days, they complete 20/24 = 5/6 of the work. Remaining = 1/6.

A can complete a work in 8 days, B can complete it in 12 days. If they work together for 4 days, how much work is left?

A can complete a work in 8 days, B can complete it in 12 days. If they work together for 4 days, how much work is left?

Step 1: Determine how much work A can do in one day. A can complete the work in 8 days, so A's rate is 1/8 of the work per day.
Step 2: Determine how much work B can do in one day. B can complete the work in 12 days, so B's rate is 1/12 of the work per day.
Step 3: Add A's rate and B's rate to find their combined rate. Combined rate = 1/8 + 1/12.
Step 4: To add the fractions, find a common denominator. The least common multiple of 8 and 12 is 24.
Step 5: Convert A's rate to the common denominator: 1/8 = 3/24. Convert B's rate to the common denominator: 1/12 = 2/24.
Step 6: Now add the two rates: 3/24 + 2/24 = 5/24. This means together they can complete 5/24 of the work in one day.
Step 7: Calculate how much work they complete in 4 days. Multiply their combined rate by 4: (5/24) * 4 = 20/24.
Step 8: Simplify 20/24 to 5/6. This means they have completed 5/6 of the work in 4 days.
Step 9: To find out how much work is left, subtract the completed work from the total work: 1 - 5/6 = 1/6.
Step 10: Therefore, the amount of work left is 1/6.

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