Time and Work
Math MCQs

Question :    If Charles can finish the work in 23 days and Kenneth can finish the same work in 28 days, then in how many days both can finish the work together?

Correct Answer  12 ³²/₅₁ days or 12.627 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Charles = 23 days

And, the number of days to finish the same work by Kenneth = 28 days

Thus, the number of days to finish the work by Charles and Kenneth together = ?

Here,

∵ In 23 days the work done by Charles = 1

∴ In 1 day, the work done by Charles = ¹/₂₃ part

Similarly,

∵ In 28 days the work done by Kenneth = 1

∴ In 1 day, the work done by Kenneth = ¹/₂₈ part

Now, in 1 day, the work done by Charles and Kenneth together

= In 1 day work done by Charles + In 1 day the work done by Kenneth

= ¹/₂₃ + ¹/₂₈

= ^{28 + 23}/₆₄₄

= ⁵¹/₆₄₄ part of work

This means in 1 day, ⁵¹/₆₄₄ part of work is done by Charles and Kenneth working together.

Now, the number of days required to finish ⁵¹/₆₄₄ part of work by Charles + Kenneth working together = 1

∴ the number of days required to finish 1 work by Charles + Kenneth together

= ¹/_⁵¹/644

= 1 × ⁶⁴⁴/₅₁ = ⁶⁴⁴/₅₁ days

= 12 ³²/₅₁ days = or 12.627 days

Thus, Charles and Kenneth working together will finish the work in 12 ³²/₅₁ days = or 12.627 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 Charles = 23 days

And the number of days required to finish the same work by Kenneth = 28 days

Thus, the number of days required to finish the work Charles and Kenneth working together = ?

Here a = 23 days

And, b = 28 days

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

The number of days required to finish the work when Charles and Kenneth working together

= ^{23 × 28}/_{23 + 28} days

= ⁶⁴⁴/₅₁ days

= 12 ³²/₅₁ days or 12.627

Thus, Charles and Kenneth together will finish the work in 12 ³²/₅₁ days or 12.627 days Answer

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