A and B can do a piece of work in 12 days and 18 days respectively. If they work

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Question: A and B can do a piece of work in 12 days and 18 days respectively. If they work together for 6 days, how much of the work is left?

Options:

Correct Answer: 1/2

Solution:

A\'s rate = 1/12, B\'s rate = 1/18. Combined rate = 1/12 + 1/18 = 5/36. In 6 days, they complete 5/6 of the work, leaving 1/6.

A and B can do a piece of work in 12 days and 18 days respectively. If they work together for 6 days, how much of the work is left?

A and B can do a piece of work in 12 days and 18 days respectively. If they work together for 6 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 12 days, so A's rate is 1/12 of the work per day.
Step 2: Determine how much work B can do in one day. B can complete the work in 18 days, so B's rate is 1/18 of the work per day.
Step 3: Add A's rate and B's rate to find their combined rate. Combined rate = 1/12 + 1/18.
Step 4: To add the fractions, find a common denominator. The least common multiple of 12 and 18 is 36.
Step 5: Convert A's rate to have a denominator of 36: 1/12 = 3/36.
Step 6: Convert B's rate to have a denominator of 36: 1/18 = 2/36.
Step 7: Now add the two rates: 3/36 + 2/36 = 5/36. This is their combined work rate per day.
Step 8: Calculate how much work they complete together in 6 days. Work done in 6 days = 6 * (5/36) = 30/36.
Step 9: Simplify 30/36 to 5/6. This means they complete 5/6 of the work in 6 days.
Step 10: To find out how much work is left, subtract the completed work from the total work: 1 - 5/6 = 1/6.

Work Rate Calculation – Understanding how to calculate individual work rates and combine them to find the total work done.
Fraction of Work Done – Calculating the fraction of work completed over a given time period.
Remaining Work – Determining the amount of work left after a certain period of collaboration.