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

Similar Questions

(1) Brian can finish a work in 49 days. Timothy can finish the same work in 54 days while Ronald can finish the work in 59 days. How long will it take to finish it if they work together?

(2) Susan can finish a work in 14 days. Jessica can finish the same work in 15 days while Sarah can finish the work in 16 days. How long will it take to finish it if they work together?

(3) Samantha can finish a work in 86 days. Christine can finish the same work in 91 days while Debra can finish the work in 96 days. How long will it take to finish it if they work together?

(4) If Charles can finish the work in 20 days and Kenneth can finish the same work in 24 days, then in how many days both can finish the work together?

(5) Margaret can finish a work in 32 days. Ashley can finish the same work in 37 days while Kimberly can finish the work in 42 days. How long will it take to finish it if they work together?

(6) If Donna can finish the work in 39 days and Brandon can finish the same work in 42 days, then in how many days both can finish the work together?

(7) If Kevin can finish the work in 44 days and Frank can finish the same work in 48 days, then in how many days both can finish the work together?

(8) If Jennifer can finish the work in 29 days and Joseph can finish the same work in 45 days, then in how many days both can finish the work together?

(9) If Matthew can finish the work in 29 days and Edward can finish the same work in 34 days, then in how many days both can finish the work together?

(10) Laura can finish a work in 62 days. Kathleen can finish the same work in 67 days while Amy can finish the work in 72 days. How long will it take to finish it if they work together?