A can do a piece of work in 12 days, while B can do it in 15 days. If they work

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What’s inside this PDF?

Question: A can do a piece of work in 12 days, while B can do it in 15 days. If they work together, how many days will they take to finish the work?

Options:

6 days
7 days
8 days
9 days

Correct Answer: 8 days

Solution:

A\'s rate = 1/12, B\'s rate = 1/15. Combined rate = 1/12 + 1/15 = 1/60. They will finish the work in 60 days.

A can do a piece of work in 12 days, while B can do it in 15 days. If they work

Practice Questions

A can do a piece of work in 12 days, while B can do it in 15 days. If they work together, how many days will they take to finish the work?

6 days
7 days
8 days
9 days

Questions & Step-by-Step Solutions

A can do a piece of work in 12 days, while B can do it in 15 days. If they work together, how many days will they take to finish the work?

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 15 days, so B's rate is 1/15 of the work per day.
Step 3: Add A's rate and B's rate together to find their combined rate. This is done by calculating 1/12 + 1/15.
Step 4: To add 1/12 and 1/15, find a common denominator. The least common multiple of 12 and 15 is 60.
Step 5: Convert 1/12 to a fraction with a denominator of 60. 1/12 = 5/60.
Step 6: Convert 1/15 to a fraction with a denominator of 60. 1/15 = 4/60.
Step 7: Now add the two fractions: 5/60 + 4/60 = 9/60.
Step 8: Simplify 9/60 to 3/20. This means together, A and B can complete 3/20 of the work in one day.
Step 9: To find out how many days they will take to finish the work, take the reciprocal of their combined rate: 1 / (3/20) = 20/3 days.
Step 10: 20/3 days is approximately 6.67 days, which means they will finish the work in about 6 days and 16 hours.

Work Rate – Understanding how to calculate the work rate of individuals and their combined work rate.
Fraction Addition – Adding fractions with different denominators to find a common work rate.
Reciprocal Calculation – Calculating the total time taken to complete work based on combined work rates.

A can do a piece of work in 12 days, while B can do it in 15 days. If they work

What’s inside this PDF?

A can do a piece of work in 12 days, while B can do it in 15 days. If they work

Practice Questions

Questions & Step-by-Step Solutions

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