A and B can complete a work in 24 days and 36 days respectively. How long will t

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Question: A and B can complete a work in 24 days and 36 days respectively. How long will they take to complete the work together?

Options:

Correct Answer: 12 days

Solution:

A\'s rate = 1/24, B\'s rate = 1/36. Combined rate = 1/24 + 1/36 = 1/15. They will complete the work in 15 days.

A and B can complete a work in 24 days and 36 days respectively. How long will they take to complete the work together?

A and B can complete a work in 24 days and 36 days respectively. How long will they take to complete the work together?

Step 1: Determine how much work A can do in one day. A can complete the work in 24 days, so A's rate is 1/24 of the work per day.
Step 2: Determine how much work B can do in one day. B can complete the work in 36 days, so B's rate is 1/36 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 1/24 + 1/36.
Step 4: To add 1/24 and 1/36, find a common denominator. The least common multiple of 24 and 36 is 72.
Step 5: Convert 1/24 to a fraction with a denominator of 72. 1/24 = 3/72.
Step 6: Convert 1/36 to a fraction with a denominator of 72. 1/36 = 2/72.
Step 7: Now add the two fractions: 3/72 + 2/72 = 5/72.
Step 8: The combined rate of A and B is 5/72 of the work per day.
Step 9: To find out how many days it will take them to complete the work together, take the reciprocal of their combined rate: 1 / (5/72) = 72/5 days.
Step 10: Calculate 72/5 to get the final answer. 72 divided by 5 equals 14.4 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 – Applying the concept of adding fractions to find a common work rate.