Time and Work
Math MCQs

Question :    If Joshua can finish the work in 40 days and Benjamin can finish the same work in 44 days, then in how many days both can finish the work together?

Correct Answer  20 ²⁰/₂₁ days or 20.952 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Joshua = 40 days

And, the number of days to finish the same work by Benjamin = 44 days

Thus, the number of days to finish the work by Joshua and Benjamin together = ?

Here,

∵ In 40 days the work done by Joshua = 1

∴ In 1 day, the work done by Joshua = ¹/₄₀ part

Similarly,

∵ In 44 days the work done by Benjamin = 1

∴ In 1 day, the work done by Benjamin = ¹/₄₄ part

Now, in 1 day, the work done by Joshua and Benjamin together

= In 1 day work done by Joshua + In 1 day the work done by Benjamin

= ¹/₄₀ + ¹/₄₄

= ^{11 + 10}/₄₄₀

= ²¹/₄₄₀ part of work

This means in 1 day, ²¹/₄₄₀ part of work is done by Joshua and Benjamin working together.

Now, the number of days required to finish ²¹/₄₄₀ part of work by Joshua + Benjamin working together = 1

∴ the number of days required to finish 1 work by Joshua + Benjamin together

= ¹/_²¹/440

= 1 × ⁴⁴⁰/₂₁ = ⁴⁴⁰/₂₁ days

= 20 ²⁰/₂₁ days = or 20.952 days

Thus, Joshua and Benjamin working together will finish the work in 20 ²⁰/₂₁ days = or 20.952 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 Joshua = 40 days

And the number of days required to finish the same work by Benjamin = 44 days

Thus, the number of days required to finish the work Joshua and Benjamin working together = ?

Here a = 40 days

And, b = 44 days

Thus, using formula ^{a × b}/_{a + b} days

The number of days required to finish the work when Joshua and Benjamin working together

= ^{40 × 44}/_{40 + 44} days

= ¹⁷⁶⁰/₈₄ days

= ^{1760 ÷ 4}/_{84 ÷ 4} = ⁴⁴⁰/₂₁ days

= 20 ²⁰/₂₁ days or 20.952

Thus, Joshua and Benjamin together will finish the work in 20 ²⁰/₂₁ days or 20.952 days Answer

Similar Questions

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(2) 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?

(3) 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?

(4) If Jennifer can finish the work in 7 days and Joseph can finish the same work in 11 days, then in how many days both can finish the work together?

(5) Amanda can finish a work in 48 days. Melissa can finish the same work in 53 days while Deborah can finish the work in 58 days. How long will it take to finish it if they work together?

(6) If Robert can finish a work in 4 days and Bob can finish the same work in 6 days, then in how many days they both can finish the work working together?

(7) If Patricia can finish the work in 5 days and William can finish the same work in 9 days, then in how many days both can finish the work together?

(8) If Brian can finish the work in 49 days and Raymond can finish the same work in 54 days, then in how many days both can finish the work together?

(9) If Joshua can finish the work in 43 days and Benjamin can finish the same work in 48 days, then in how many days both can finish the work together?

(10) Samantha can finish a work in 86 days. Christine can finish the same work in 91 days while Debra can finish the work in 96 days. How long will it take to finish it if they work together?