Time and Work
Math MCQs

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 & 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

(1) If Betty can finish the work in 30 days and Jason can finish the same work in 35 days, then in how many days both can finish the work together?

(2) If John can finish the work in 9 days and Richard can finish the same work in 14 days, then in how many days both can finish the work together?

(3) 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?

(4) If Sandra can finish the work in 31 days and Gary can finish the same work in 34 days, then in how many days both can finish the work together?

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(6) Jack can finish a work in 99 days. Jerry can finish the same work in 104 days while Tyler can finish the work in 109 days. How long will it take to finish it if they work together?

(7) Carol can finish a work in 42 days. Amanda can finish the same work in 43 days while Dorothy can finish the work in 44 days. How long will it take to finish it if they work together?

(8) If A can do a piece of work in 2 days, B can do the same piece of work in 3 days, while C alone can do the same work in 4 days. Find the number of days to finish the work when they all will work together.

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