A and B can complete work together in 5 days. If a works at twice his speed and B at half of his speed this wo

Question

A and B can complete work together in 5 days. If a works at twice his speed and B at half of his speed this works can be finished in 4 days. How many days would it take for A alone to complete the job?

Accepted Answer

Let the efficiency of A be x and B be y.

According to the first condition, work is completed in 5 days when both work together.
Total Work = 5 times (x plus y)

According to the second condition, if A works at double speed and B at half speed, work is finished in 4 days.
Total Work = 4 times (2x plus y divided by 2)

Equating both expressions for Total Work:
5x plus 5y = 8x plus 2y
3x = 3y
x = y

This means A and B have equal efficiency.

Now substitute x = y into the first Total Work equation:
Total Work = 5 times (x plus x) = 10x

To find the time taken by A alone, divide Total Work by A efficiency:
Time = 10x divided by x = 10 days.

Therefore, A alone can complete the work in 10 days.

Answer

10

Answer

12

Answer

15

Answer

18

A and B can complete work together in 5 days. If a works at twice his speed and B at half of his speed this works can be finished in 4 days. How many days would it take for A alone to complete the job?

Explanation

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