Time and Work
Math MCQs

Question :    If Michelle can finish the work in 41 days and Samuel can finish the same work in 45 days, then in how many days both can finish the work together?

Correct Answer  21 ³⁹/₈₆ days or 21.453 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Michelle = 41 days

And, the number of days to finish the same work by Samuel = 45 days

Thus, the number of days to finish the work by Michelle and Samuel together = ?

Here,

∵ In 41 days the work done by Michelle = 1

∴ In 1 day, the work done by Michelle = ¹/₄₁ part

Similarly,

∵ In 45 days the work done by Samuel = 1

∴ In 1 day, the work done by Samuel = ¹/₄₅ part

Now, in 1 day, the work done by Michelle and Samuel together

= In 1 day work done by Michelle + In 1 day the work done by Samuel

= ¹/₄₁ + ¹/₄₅

= ^{45 + 41}/₁₈₄₅

= ⁸⁶/₁₈₄₅ part of work

This means in 1 day, ⁸⁶/₁₈₄₅ part of work is done by Michelle and Samuel working together.

Now, the number of days required to finish ⁸⁶/₁₈₄₅ part of work by Michelle + Samuel working together = 1

∴ the number of days required to finish 1 work by Michelle + Samuel together

= ¹/_⁸⁶/1845

= 1 × ¹⁸⁴⁵/₈₆ = ¹⁸⁴⁵/₈₆ days

= 21 ³⁹/₈₆ days = or 21.453 days

Thus, Michelle and Samuel working together will finish the work in 21 ³⁹/₈₆ days = or 21.453 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 Michelle = 41 days

And the number of days required to finish the same work by Samuel = 45 days

Thus, the number of days required to finish the work Michelle and Samuel working together = ?

Here a = 41 days

And, b = 45 days

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

The number of days required to finish the work when Michelle and Samuel working together

= ^{41 × 45}/_{41 + 45} days

= ¹⁸⁴⁵/₈₆ days

= 21 ³⁹/₈₆ days or 21.453

Thus, Michelle and Samuel together will finish the work in 21 ³⁹/₈₆ days or 21.453 days Answer

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