Time and Work
Math MCQs

Question :    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?

Correct Answer  22 ⁶²/₉₁ days or 22.681 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Joshua = 43 days

And, the number of days to finish the same work by Benjamin = 48 days

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

Here,

∵ In 43 days the work done by Joshua = 1

∴ In 1 day, the work done by Joshua = ¹/₄₃ part

Similarly,

∵ In 48 days the work done by Benjamin = 1

∴ In 1 day, the work done by Benjamin = ¹/₄₈ 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

= ¹/₄₃ + ¹/₄₈

= ^{48 + 43}/₂₀₆₄

= ⁹¹/₂₀₆₄ part of work

This means in 1 day, ⁹¹/₂₀₆₄ part of work is done by Joshua and Benjamin working together.

Now, the number of days required to finish ⁹¹/₂₀₆₄ part of work by Joshua + Benjamin working together = 1

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

= ¹/_⁹¹/2064

= 1 × ²⁰⁶⁴/₉₁ = ²⁰⁶⁴/₉₁ days

= 22 ⁶²/₉₁ days = or 22.681 days

Thus, Joshua and Benjamin working together will finish the work in 22 ⁶²/₉₁ days = or 22.681 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 = 43 days

And the number of days required to finish the same work by Benjamin = 48 days

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

Here a = 43 days

And, b = 48 days

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

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

= ^{43 × 48}/_{43 + 48} days

= ²⁰⁶⁴/₉₁ days

= 22 ⁶²/₉₁ days or 22.681

Thus, Joshua and Benjamin together will finish the work in 22 ⁶²/₉₁ days or 22.681 days Answer

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