Time and Work
MCQs Math


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 And 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

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(2) Katherine can finish a work in 88 days. Debra can finish the same work in 93 days while Rachel can finish the work in 98 days. How long will it take to finish it if they work together?

(3) Andrew can finish a work in 37 days. Joshua can finish the same work in 38 days while Kenneth can finish the work in 39 days. How long will it take to finish it if they work together?

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(7) If Kevin can finish the work in 47 days and Frank can finish the same work in 52 days, then in how many days both can finish the work together?

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