Time and Work
Math MCQs

Question :    If Donna can finish the work in 39 days and Brandon can finish the same work in 43 days, then in how many days both can finish the work together?

Correct Answer  20 ³⁷/₈₂ days or 20.451 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Donna = 39 days

And, the number of days to finish the same work by Brandon = 43 days

Thus, the number of days to finish the work by Donna and Brandon together = ?

Here,

∵ In 39 days the work done by Donna = 1

∴ In 1 day, the work done by Donna = ¹/₃₉ part

Similarly,

∵ In 43 days the work done by Brandon = 1

∴ In 1 day, the work done by Brandon = ¹/₄₃ part

Now, in 1 day, the work done by Donna and Brandon together

= In 1 day work done by Donna + In 1 day the work done by Brandon

= ¹/₃₉ + ¹/₄₃

= ^{43 + 39}/₁₆₇₇

= ⁸²/₁₆₇₇ part of work

This means in 1 day, ⁸²/₁₆₇₇ part of work is done by Donna and Brandon working together.

Now, the number of days required to finish ⁸²/₁₆₇₇ part of work by Donna + Brandon working together = 1

∴ the number of days required to finish 1 work by Donna + Brandon together

= ¹/_⁸²/1677

= 1 × ¹⁶⁷⁷/₈₂ = ¹⁶⁷⁷/₈₂ days

= 20 ³⁷/₈₂ days = or 20.451 days

Thus, Donna and Brandon working together will finish the work in 20 ³⁷/₈₂ days = or 20.451 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 Donna = 39 days

And the number of days required to finish the same work by Brandon = 43 days

Thus, the number of days required to finish the work Donna and Brandon working together = ?

Here a = 39 days

And, b = 43 days

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

The number of days required to finish the work when Donna and Brandon working together

= ^{39 × 43}/_{39 + 43} days

= ¹⁶⁷⁷/₈₂ days

= 20 ³⁷/₈₂ days or 20.451

Thus, Donna and Brandon together will finish the work in 20 ³⁷/₈₂ days or 20.451 days Answer

Similar Questions

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