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

(1) If David can finish the work in 32 days and Christopher can finish the same work in 48 days, then in how many days both can finish the work together?

(2) If Ryan can finish the work in 63 days and Ethan can finish the same work in 68 days, then in how many days both can finish the work together?

(3) If Ashley can finish the work in 33 days and Eric can finish the same work in 36 days, then in how many days both can finish the work together?

(4) Sandra can finish a work in 34 days. Kimberly can finish the same work in 39 days while Emily can finish the work in 44 days. How long will it take to finish it if they work together?

(5) If Nancy can finish the work in 25 days and Ronald can finish the same work in 28 days, then in how many days both can finish the work together?

(6) If Nicholas can finish the work in 69 days and Roger can finish the same work in 74 days, then in how many days both can finish the work together?

(7) If Stephen can finish the work in 75 days and Carl can finish the same work in 80 days, then in how many days both can finish the work together?

(8) Michael can finish a work in 11 days. William can finish the same work in 16 days while Richard can finish the work in 21 days. How long will it take to finish it if they work together?

(9) If Jack can finish a work in 8 days and Bill can finish the same work in 12 days, then in how many days they both can finish the work working together?

(10) Nicholas can finish a work in 69 days. Jonathan can finish the same work in 74 days while Stephen can finish the work in 79 days. How long will it take to finish it if they work together?