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

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(2) Gregory can finish a work in 89 days. Frank can finish the same work in 94 days while Patrick can finish the work in 99 days. How long will it take to finish it if they work together?

(3) If Margaret can finish the work in 29 days and Ryan can finish the same work in 32 days, then in how many days both can finish the work together?

(4) If Amy can finish the work in 68 days and Keith can finish the same work in 73 days, then in how many days both can finish the work together?

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(6) If Samantha can finish the work in 86 days and Logan can finish the same work in 91 days, then in how many days both can finish the work together?

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(8) If Paul can finish the work in 39 days and Larry can finish the same work in 44 days, then in how many days both can finish the work together?

(9) If Eric can finish the work in 71 days and Gerald can finish the same work in 76 days, then in how many days both can finish the work together?

(10) William can finish a work in 15 days. Joseph can finish the same work in 20 days while Thomas can finish the work in 25 days. How long will it take to finish it if they work together?