A and B can complete a task in 10 days and 15 days respectively. If they work to

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Question: A and B can complete a task in 10 days and 15 days respectively. If they work together for 5 days, how much of the task is left?

Options:

Correct Answer: 1/3

Solution:

A\'s rate = 1/10, B\'s rate = 1/15. Combined rate = 1/10 + 1/15 = 1/6. Work done in 5 days = 5/6. Remaining = 1 - 5/6 = 1/6.

A and B can complete a task in 10 days and 15 days respectively. If they work together for 5 days, how much of the task is left?

A and B can complete a task in 10 days and 15 days respectively. If they work together for 5 days, how much of the task is left?

Correct Answer: 1/6

Step 1: Determine A's work rate. A can complete the task in 10 days, so A's rate is 1/10 of the task per day.
Step 2: Determine B's work rate. B can complete the task in 15 days, so B's rate is 1/15 of the task per day.
Step 3: Calculate the combined work rate of A and B. Add A's rate (1/10) and B's rate (1/15).
Step 4: To add the fractions, find a common denominator. The least common multiple of 10 and 15 is 30.
Step 5: Convert A's rate to the common denominator: 1/10 = 3/30.
Step 6: Convert B's rate to the common denominator: 1/15 = 2/30.
Step 7: Add the two rates: 3/30 + 2/30 = 5/30, which simplifies to 1/6.
Step 8: Calculate the total work done in 5 days. Multiply the combined rate (1/6) by 5 days: 5 * (1/6) = 5/6 of the task completed.
Step 9: Determine how much of the task is left. Subtract the work done (5/6) from the total task (1): 1 - 5/6 = 1/6.

Work Rate – Understanding how to calculate individual work rates and combine them to find the total work done.
Fraction of Work – Calculating the fraction of work completed and remaining based on the combined work rate.