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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


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