If a man can complete a work in 10 days and another in 15 days, how long will it

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Question: If a man can complete a work in 10 days and another in 15 days, how long will it take them to complete the work together?

Options:

Correct Answer: 8 days

Solution:

Work done by first man in a day = 1/10, second man = 1/15. Together = 1/10 + 1/15 = 1/6. Time = 6 days.

If a man can complete a work in 10 days and another in 15 days, how long will it take them to complete the work together?

If a man can complete a work in 10 days and another in 15 days, how long will it take them to complete the work together?

Step 1: Determine how much work each man can do in one day. The first man can complete the work in 10 days, so he does 1/10 of the work in one day.
Step 2: The second man can complete the work in 15 days, so he does 1/15 of the work in one day.
Step 3: Add the work done by both men in one day together. This is 1/10 + 1/15.
Step 4: To add 1/10 and 1/15, find a common denominator. The least common multiple of 10 and 15 is 30.
Step 5: Convert 1/10 to 3/30 and 1/15 to 2/30.
Step 6: Now add 3/30 + 2/30 = 5/30.
Step 7: Simplify 5/30 to 1/6. This means together they can complete 1/6 of the work in one day.
Step 8: To find out how many days it takes them to complete the whole work together, take the reciprocal of 1/6, which is 6 days.

Work Rate – Understanding how to calculate the work rate of individuals and combine their rates to find the total work done together.
Fraction Addition – Adding fractions with different denominators to find a common work rate.