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) If Joseph can finish the work in 19 days and Steven can finish the same work in 24 days, then in how many days both can finish the work together?

(2) Mark can finish a work in 29 days. Donald can finish the same work in 30 days while Steven can finish the work in 31 days. How long will it take to finish it if they work together?

(3) If David can finish the work in 13 days and Christopher can finish the same work in 18 days, then in how many days both can finish the work together?

(4) If Brian can finish the work in 46 days and Raymond can finish the same work in 49 days, then in how many days both can finish the work together?

(5) John can finish a work in 9 days. David can finish the same work in 14 days while William can finish the work in 19 days. How long will it take to finish it if they work together?

(6) 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?

(7) If Susan can finish the work in 15 days and Donald can finish the same work in 18 days, then in how many days both can finish the work together?

(8) If Thomas can finish the work in 18 days and Andrew can finish the same work in 21 days, then in how many days both can finish the work together?

(9) 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?

(10) If Patrick can finish the work in 95 days and Vincent can finish the same work in 100 days, then in how many days both can finish the work together?