Question

a किसी काम को 40 दिन में समाप्त करता है तथा b उसी काम को 50 दिन में समाप्त करता है। यदि दोनों बारी बारी एक एक दिन काम करे तथा a कार्य सुरु करे तो कार्य कब समाप्त होगा

Answer 1

A can finish the work in 40 days
in 1 day, he will finish = 1/40 of the work.

B can finish the work in 50 days
in 1 day, he will finish = 1/50 of the work.
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If A starts the work and they work alternately,
They will work 1 day each in every 2 days.

Let's call the work done in 2 days be 1 unit of work.

1 unit of work = 1/40 + 1/50 = (5+4)/200 = 9/200 of the work
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Total units of work = 200/9 = 22.22 units.

To finish 22 units, number of days = 22×2 = 44

remaining work = 1 - (22 × 9/200) = 1 - 198/200 = 2/200 = 1/100

This work will be done by A.
time required to finish 1/100 of work = 1/100 ÷ 1/40 = 1/100 × 40 = 2/5 days

Total days = 44 + 2/5 = 44 2/5 days