Time and Work
Math MCQs

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 & 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

(1) Karen can finish a work in 20 days. Lisa can finish the same work in 21 days while Nancy can finish the work in 22 days. How long will it take to finish it if they work together?

(2) If Gregory can finish the work in 89 days and Alan can finish the same work in 94 days, then in how many days both can finish the work together?

(3) Joseph can finish a work in 15 days. Thomas can finish the same work in 16 days while Charles can finish the work in 17 days. How long will it take to finish it if they work together?

(4) If Katherine can finish the work in 88 days and Willie can finish the same work in 93 days, then in how many days both can finish the work together?

(5) If Kenneth can finish the work in 42 days and Gregory can finish the same work in 46 days, then in how many days both can finish the work together?

(6) 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?

(7) Carol can finish a work in 46 days. Dorothy can finish the same work in 51 days while Melissa can finish the work in 56 days. How long will it take to finish it if they work together?

(8) Ryan can finish a work in 63 days. Gary can finish the same work in 68 days while Nicholas can finish the work in 73 days. How long will it take to finish it if they work together?

(9) If Jennifer can finish the work in 7 days and Joseph can finish the same work in 10 days, then in how many days both can finish the work together?

(10) If Robert can finish the work in 4 days and David can finish the same work in 8 days, then in how many days both can finish the work together?