Time and Work
Math MCQs

Question :    If Donna can finish the work in 42 days and Brandon can finish the same work in 47 days, then in how many days both can finish the work together?

Correct Answer  22 ¹⁶/₈₉ days or 22.18 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Donna = 42 days

And, the number of days to finish the same work by Brandon = 47 days

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

Here,

∵ In 42 days the work done by Donna = 1

∴ In 1 day, the work done by Donna = ¹/₄₂ part

Similarly,

∵ In 47 days the work done by Brandon = 1

∴ In 1 day, the work done by Brandon = ¹/₄₇ 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

= ¹/₄₂ + ¹/₄₇

= ^{47 + 42}/₁₉₇₄

= ⁸⁹/₁₉₇₄ part of work

This means in 1 day, ⁸⁹/₁₉₇₄ part of work is done by Donna and Brandon working together.

Now, the number of days required to finish ⁸⁹/₁₉₇₄ part of work by Donna + Brandon working together = 1

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

= ¹/_⁸⁹/1974

= 1 × ¹⁹⁷⁴/₈₉ = ¹⁹⁷⁴/₈₉ days

= 22 ¹⁶/₈₉ days = or 22.18 days

Thus, Donna and Brandon working together will finish the work in 22 ¹⁶/₈₉ days = or 22.18 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 = 42 days

And the number of days required to finish the same work by Brandon = 47 days

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

Here a = 42 days

And, b = 47 days

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

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

= ^{42 × 47}/_{42 + 47} days

= ¹⁹⁷⁴/₈₉ days

= 22 ¹⁶/₈₉ days or 22.18

Thus, Donna and Brandon together will finish the work in 22 ¹⁶/₈₉ days or 22.18 days Answer

Similar Questions

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(2) If James can finish the work in 2 days and John can finish the same work in 5 days, then in how many days both can finish the work together?

(3) Alexander can finish a work in 91 days. Patrick can finish the same work in 96 days while Raymond can finish the work in 101 days. How long will it take to finish it if they work together?

(4) Charles can finish a work in 23 days. Daniel can finish the same work in 28 days while Matthew can finish the work in 33 days. How long will it take to finish it if they work together?

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(6) If Emily can finish the work in 37 days and Justin can finish the same work in 40 days, then in how many days both can finish the work together?

(7) If A can do a piece of work in 2 days, B can do the same piece of work in 3 days, while C alone can do the same work in 4 days. Find the number of days to finish the work when they all will work together.

(8) If Elizabeth can finish the work in 11 days and Daniel can finish the same work in 14 days, then in how many days both can finish the work together?

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(10) If Christopher can finish the work in 25 days and Brian can finish the same work in 30 days, then in how many days both can finish the work together?