A and B can complete a task in 15 days and 20 days respectively. If they work to

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Question: A and B can complete a task in 15 days and 20 days respectively. If they work together for 5 days, how much of the task is left?

Options:

Correct Answer: 1/3

Solution:

A\'s work in 1 day = 1/15, B\'s work in 1 day = 1/20. Together = 1/15 + 1/20 = 7/60. In 5 days = 5 * 7/60 = 7/12. Remaining = 1 - 7/12 = 5/12.

A and B can complete a task in 15 days and 20 days respectively. If they work together for 5 days, how much of the task is left?

A and B can complete a task in 15 days and 20 days respectively. If they work together for 5 days, how much of the task is left?

Step 1: Determine how much of the task A can complete in one day. A can complete the task in 15 days, so A's work in 1 day is 1/15.
Step 2: Determine how much of the task B can complete in one day. B can complete the task in 20 days, so B's work in 1 day is 1/20.
Step 3: Add A's and B's work together to find out how much they can complete in one day when working together. This is 1/15 + 1/20.
Step 4: To add 1/15 and 1/20, find a common denominator. The least common multiple of 15 and 20 is 60. Convert the fractions: 1/15 = 4/60 and 1/20 = 3/60.
Step 5: Now add the two fractions: 4/60 + 3/60 = 7/60. This means together they can complete 7/60 of the task in one day.
Step 6: Calculate how much of the task they complete in 5 days. Multiply their combined daily work by 5: 5 * 7/60 = 35/60.
Step 7: Simplify 35/60 to 7/12. This means A and B together complete 7/12 of the task in 5 days.
Step 8: To find out how much of the task is left, subtract the completed part from the whole task: 1 - 7/12.
Step 9: Convert 1 to a fraction with a denominator of 12: 1 = 12/12. Now subtract: 12/12 - 7/12 = 5/12.
Step 10: The remaining part of the task is 5/12.

Work Rate – Understanding how to calculate individual and combined work rates to determine the amount of work completed over time.
Fraction Operations – Applying addition and subtraction of fractions to find the total work done and the remaining work.