Time and Work
Math MCQs

Question :    If Kevin can finish the work in 44 days and Frank can finish the same work in 47 days, then in how many days both can finish the work together?

Correct Answer  22 ⁶⁶/₉₁ days or 22.725 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Kevin = 44 days

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

Thus, the number of days to finish the work by Kevin and Frank together = ?

Here,

∵ In 44 days the work done by Kevin = 1

∴ In 1 day, the work done by Kevin = ¹/₄₄ part

Similarly,

∵ In 47 days the work done by Frank = 1

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

Now, in 1 day, the work done by Kevin and Frank together

= In 1 day work done by Kevin + In 1 day the work done by Frank

= ¹/₄₄ + ¹/₄₇

= ^{47 + 44}/₂₀₆₈

= ⁹¹/₂₀₆₈ part of work

This means in 1 day, ⁹¹/₂₀₆₈ part of work is done by Kevin and Frank working together.

Now, the number of days required to finish ⁹¹/₂₀₆₈ part of work by Kevin + Frank working together = 1

∴ the number of days required to finish 1 work by Kevin + Frank together

= ¹/_⁹¹/2068

= 1 × ²⁰⁶⁸/₉₁ = ²⁰⁶⁸/₉₁ days

= 22 ⁶⁶/₉₁ days = or 22.725 days

Thus, Kevin and Frank working together will finish the work in 22 ⁶⁶/₉₁ days = or 22.725 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 Kevin = 44 days

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

Thus, the number of days required to finish the work Kevin and Frank working together = ?

Here a = 44 days

And, b = 47 days

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

The number of days required to finish the work when Kevin and Frank working together

= ^{44 × 47}/_{44 + 47} days

= ²⁰⁶⁸/₉₁ days

= 22 ⁶⁶/₉₁ days or 22.725

Thus, Kevin and Frank together will finish the work in 22 ⁶⁶/₉₁ days or 22.725 days Answer

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