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

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

Options:

Correct Answer: 8 days

Solution:

Work done in one day = 1/10 + 1/15 = 1/6. Therefore, they will complete the work in 6 days.

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

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

Step 1: Understand that the man who can complete the work in 10 days does 1/10 of the work in one day.
Step 2: Understand that the man who can complete the work in 15 days does 1/15 of the work in one day.
Step 3: Add the work done by both men in one day: 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 (because 1 * 3 = 3 and 10 * 3 = 30).
Step 6: Convert 1/15 to 2/30 (because 1 * 2 = 2 and 15 * 2 = 30).
Step 7: Now add the two fractions: 3/30 + 2/30 = 5/30.
Step 8: Simplify 5/30 to 1/6 (by dividing both the numerator and denominator by 5).
Step 9: This means together they complete 1/6 of the work in one day.
Step 10: To find out how many days they take to complete the whole work, take the reciprocal of 1/6, which is 6.
Step 11: Therefore, they will complete the work together in 6 days.

Work Rate – Understanding how to calculate the combined work rate of two individuals working together.
Fraction Addition – Applying the concept of adding fractions to determine the total work done in a day.