A can do a work in 40 days, B can do it in 60 days. How long will they take to c

₹0.0

Question: A can do a work in 40 days, B can do it in 60 days. How long will they take to complete the work together?

Options:

Correct Answer: 24 days

Solution:

A\'s rate = 1/40, B\'s rate = 1/60. Combined rate = 1/40 + 1/60 = 1/24. They will finish the work in 24 days.

A can do a work in 40 days, B can do it in 60 days. How long will they take to complete the work together?

A can do a work in 40 days, B can do it in 60 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 40 days, A's rate is 1/40 of the work per day.
Step 2: Determine how much work B can do in one day. Since B can complete the work in 60 days, B's rate is 1/60 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 1/40 + 1/60.
Step 4: To add the fractions, find a common denominator. The least common multiple of 40 and 60 is 120.
Step 5: Convert A's rate to the common denominator: 1/40 = 3/120.
Step 6: Convert B's rate to the common denominator: 1/60 = 2/120.
Step 7: Now add the two rates: 3/120 + 2/120 = 5/120.
Step 8: Simplify the combined rate: 5/120 = 1/24.
Step 9: The combined rate of 1/24 means they can complete 1 whole work in 24 days when working together.

Work Rate – Understanding how to calculate the work rate of individuals and combine their rates to find the total time taken to complete a task.
Fraction Addition – Applying the concept of adding fractions to determine the combined work rate of A and B.