If A can complete a work in 10 days and B can complete the same work in 15 days,

₹0.0

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

Options:

Correct Answer: 6 days

Solution:

A\'s work rate = 1/10, B\'s work rate = 1/15. Together, they work at (1/10 + 1/15) = 1/6. Therefore, they will complete the work in 6 days.

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

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

Step 1: Determine how much work A can do in one day. Since A can complete the work in 10 days, A's work rate is 1/10 of the work per day.
Step 2: Determine how much work B can do in one day. Since B can complete the work in 15 days, B's work rate is 1/15 of the work per day.
Step 3: Add A's work rate and B's work rate together to find their combined work rate. 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. Now add them: 3/30 + 2/30 = 5/30.
Step 6: Simplify 5/30 to 1/6. This means together, A and B can complete 1/6 of the work in one day.
Step 7: To find out how many days it takes to complete the entire work, take the reciprocal of 1/6. This gives you 6 days.

Work Rate – Understanding how to calculate individual work rates and combine them to find the total work rate when multiple workers are involved.
Fraction Addition – Adding fractions with different denominators to find a common work rate.
Time Calculation – Calculating the total time taken to complete a task based on combined work rates.