Time and Work
Math MCQs

Question :    If Brenda can finish the work in 76 days and Arthur can finish the same work in 81 days, then in how many days both can finish the work together?

Correct Answer  39 ³³/₁₅₇ days or 39.21 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Brenda = 76 days

And, the number of days to finish the same work by Arthur = 81 days

Thus, the number of days to finish the work by Brenda and Arthur together = ?

Here,

∵ In 76 days the work done by Brenda = 1

∴ In 1 day, the work done by Brenda = ¹/₇₆ part

Similarly,

∵ In 81 days the work done by Arthur = 1

∴ In 1 day, the work done by Arthur = ¹/₈₁ part

Now, in 1 day, the work done by Brenda and Arthur together

= In 1 day work done by Brenda + In 1 day the work done by Arthur

= ¹/₇₆ + ¹/₈₁

= ^{81 + 76}/₆₁₅₆

= ¹⁵⁷/₆₁₅₆ part of work

This means in 1 day, ¹⁵⁷/₆₁₅₆ part of work is done by Brenda and Arthur working together.

Now, the number of days required to finish ¹⁵⁷/₆₁₅₆ part of work by Brenda + Arthur working together = 1

∴ the number of days required to finish 1 work by Brenda + Arthur together

= ¹/_{¹⁵⁷/6156}

= 1 × ⁶¹⁵⁶/₁₅₇ = ⁶¹⁵⁶/₁₅₇ days

= 39 ³³/₁₅₇ days = or 39.21 days

Thus, Brenda and Arthur working together will finish the work in 39 ³³/₁₅₇ days = or 39.21 days Answer

Shortcut Trick to solve the problems based on time and work using formula

Case: If A can finish a work in a days, and B can finish the same work in b days,
then working together the number of days require to finish the work
= ^{a × b}/_{a + b} days.

Here given,

The number of days required to finish the work by Brenda = 76 days

And the number of days required to finish the same work by Arthur = 81 days

Thus, the number of days required to finish the work Brenda and Arthur working together = ?

Here a = 76 days

And, b = 81 days

Thus, using formula ^{a × b}/_{a + b} days

The number of days required to finish the work when Brenda and Arthur working together

= ^{76 × 81}/_{76 + 81} days

= ⁶¹⁵⁶/₁₅₇ days

= 39 ³³/₁₅₇ days or 39.21

Thus, Brenda and Arthur together will finish the work in 39 ³³/₁₅₇ days or 39.21 days Answer

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