Time and Work
Math MCQs

Question :    If Mary can finish the work in 25 days and Michael can finish the same work in 41 days, then in how many days both can finish the work together?

Correct Answer  15 ³⁵/₆₆ days or 15.53 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Mary = 25 days

And, the number of days to finish the same work by Michael = 41 days

Thus, the number of days to finish the work by Mary and Michael together = ?

Here,

∵ In 25 days the work done by Mary = 1

∴ In 1 day, the work done by Mary = ¹/₂₅ part

Similarly,

∵ In 41 days the work done by Michael = 1

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

Now, in 1 day, the work done by Mary and Michael together

= In 1 day work done by Mary + In 1 day the work done by Michael

= ¹/₂₅ + ¹/₄₁

= ^{41 + 25}/₁₀₂₅

= ⁶⁶/₁₀₂₅ part of work

This means in 1 day, ⁶⁶/₁₀₂₅ part of work is done by Mary and Michael working together.

Now, the number of days required to finish ⁶⁶/₁₀₂₅ part of work by Mary + Michael working together = 1

∴ the number of days required to finish 1 work by Mary + Michael together

= ¹/_⁶⁶/1025

= 1 × ¹⁰²⁵/₆₆ = ¹⁰²⁵/₆₆ days

= 15 ³⁵/₆₆ days = or 15.53 days

Thus, Mary and Michael working together will finish the work in 15 ³⁵/₆₆ days = or 15.53 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 Mary = 25 days

And the number of days required to finish the same work by Michael = 41 days

Thus, the number of days required to finish the work Mary and Michael working together = ?

Here a = 25 days

And, b = 41 days

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

The number of days required to finish the work when Mary and Michael working together

= ^{25 × 41}/_{25 + 41} days

= ¹⁰²⁵/₆₆ days

= 15 ³⁵/₆₆ days or 15.53

Thus, Mary and Michael together will finish the work in 15 ³⁵/₆₆ days or 15.53 days Answer

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