If A can complete a work in 14 days and B can complete it in 21 days, how long w

₹0.0

Question: If A can complete a work in 14 days and B can complete it in 21 days, how long will they take to complete the work together?

Options:

Correct Answer: 9 days

Solution:

A\'s rate = 1/14, B\'s rate = 1/21. Combined rate = 1/14 + 1/21 = 1/10. They will finish the work in 10 days.

If A can complete a work in 14 days and B can complete it in 21 days, how long will they take to complete the work together?

If A can complete a work in 14 days and B can complete it in 21 days, 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 14 days, so A's rate is 1/14 of the work per day.
Step 2: Determine how much work B can do in one day. B can complete the work in 21 days, so B's rate is 1/21 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 1/14 + 1/21.
Step 4: To add 1/14 and 1/21, find a common denominator. The least common multiple of 14 and 21 is 42.
Step 5: Convert 1/14 to a fraction with a denominator of 42. This is 3/42.
Step 6: Convert 1/21 to a fraction with a denominator of 42. This is 2/42.
Step 7: Now add the two fractions: 3/42 + 2/42 = 5/42.
Step 8: The combined rate of A and B is 5/42 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 / (5/42) = 42/5 days.
Step 10: Calculate 42/5 days, which is equal to 8.4 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.