Time and Work
MCQs Math


Question:     If Charles can finish the work in 20 days and Kenneth can finish the same work in 23 days, then in how many days both can finish the work together?


Correct Answer  10 30/43 days or 10.698 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Charles = 20 days

And, the number of days to finish the same work by Kenneth = 23 days

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

Here,

∵ In 20 days the work done by Charles = 1

∴ In 1 day, the work done by Charles = 1/20 part

Similarly,

∵ In 23 days the work done by Kenneth = 1

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

= 1/20 + 1/23

= 23 + 20/460

= 43/460 part of work

This means in 1 day, 43/460 part of work is done by Charles and Kenneth working together.

Now, the number of days required to finish 43/460 part of work by Charles + Kenneth working together = 1

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

= 1/43/460

= 1 × 460/43 = 460/43 days

= 10 30/43 days = or 10.698 days

Thus, Charles and Kenneth working together will finish the work in 10 30/43 days = or 10.698 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 = 20 days

And the number of days required to finish the same work by Kenneth = 23 days

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

Here a = 20 days

And, b = 23 days

Thus, using formula a × b/a + b days

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

= 20 × 23/20 + 23 days

= 460/43 days

= 10 30/43 days or 10.698

Thus, Charles and Kenneth together will finish the work in 10 30/43 days or 10.698 days Answer


Similar Questions

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(2) If Paul can finish the work in 36 days and Larry can finish the same work in 40 days, then in how many days both can finish the work together?

(3) If Mary can finish the work in 6 days and Michael can finish the same work in 11 days, then in how many days both can finish the work together?

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