Question

A can do a piece of work in 8 days working 10 hours a day. B can do the same work in 10 days working 8 hours a day. In how many days will they both do it together working 8 hours a day?​

Answer 1

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A and B can complete the work in 5 days.

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• A can complete the work in 8 days(working 10 hours per day).

• B can complete the work in 10 days(working 8 hours per day).

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Total no. of days A & B together will take to finish the work(at a rate of 8 hours per day).

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According to the question,

A can do work in 8 days at the rate of 10 hours a day.

∴ A completes work in 8 × 10 = 80 hours.

∴ A completes the work in 80 hours.

∴ A can do work in one hour = 1/80

Similarly,

B can do the same work in 10 days at the rate of 8 hours a day.

∴ B can do the same work in 10 × 8 = 80 hours

∴ B can do the work in 80 hours.

∴ B can do work in one hour = 1/80

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Now, A & B combines together to do work.

A' s work in one hour = 1/80

B' s work in one hour = 1/80

∴ (A + B)' s work in one hour = 1/80 + 1/80

= 1 + 1/80

= 2/80

= 1/40

∴ A and B can do work in one hour = 1/40

∴ Total No. of hours required to complete the work by A & B = 1/1/40 = 1 × 40/1 = 40 hours.

∴ A & B complete the work in 40 hours.

Now, A & B together works at a rate of 8 hours per day.

∴ No. of days required for them = 40 hours/8 hours per day = 5 days

∴ A & B can complete the work in 5 days.