Time and Work
MCQs Math


Question:     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?


Correct Answer  10 10/11 days or 10.909 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 = 24 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 24 days the work done by Kenneth = 1

∴ In 1 day, the work done by Kenneth = 1/24 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 + 1/24

= 6 + 5/120

= 11/120 part of work

This means in 1 day, 11/120 part of work is done by Charles and Kenneth working together.

Now, the number of days required to finish 11/120 part of work by Charles + Kenneth working together = 1

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

= 1/11/120

= 1 × 120/11 = 120/11 days

= 10 10/11 days = or 10.909 days

Thus, Charles and Kenneth working together will finish the work in 10 10/11 days = or 10.909 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 = 24 days

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

Here a = 20 days

And, b = 24 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 × 24/20 + 24 days

= 480/44 days

= 480 ÷ 4/44 ÷ 4 = 120/11 days

= 10 10/11 days or 10.909

Thus, Charles and Kenneth together will finish the work in 10 10/11 days or 10.909 days Answer


Similar Questions

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(6) Mark can finish a work in 33 days. Steven can finish the same work in 38 days while Paul can finish the work in 43 days. How long will it take to finish it if they work together?

(7) If Patricia can finish the work in 5 days and William can finish the same work in 8 days, then in how many days both can finish the work together?

(8) If James can finish the work in 2 days and John can finish the same work in 5 days, then in how many days both can finish the work together?

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