Time and Work
Math MCQs

Question :    If Joshua can finish the work in 40 days and Benjamin can finish the same work in 43 days, then in how many days both can finish the work together?

Correct Answer  20 ⁶⁰/₈₃ days or 20.723 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 = 43 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 43 days the work done by Benjamin = 1

∴ In 1 day, the work done by Benjamin = ¹/₄₃ 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 + ¹/₄₃

= ^{43 + 40}/₁₇₂₀

= ⁸³/₁₇₂₀ part of work

This means in 1 day, ⁸³/₁₇₂₀ part of work is done by Joshua and Benjamin working together.

Now, the number of days required to finish ⁸³/₁₇₂₀ part of work by Joshua + Benjamin working together = 1

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

= ¹/_⁸³/1720

= 1 × ¹⁷²⁰/₈₃ = ¹⁷²⁰/₈₃ days

= 20 ⁶⁰/₈₃ days = or 20.723 days

Thus, Joshua and Benjamin working together will finish the work in 20 ⁶⁰/₈₃ days = or 20.723 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 = 43 days

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

Here a = 40 days

And, b = 43 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 × 43}/_{40 + 43} days

= ¹⁷²⁰/₈₃ days

= 20 ⁶⁰/₈₃ days or 20.723

Thus, Joshua and Benjamin together will finish the work in 20 ⁶⁰/₈₃ days or 20.723 days Answer

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