Time and Work
Math MCQs

Question :    If Emma can finish the work in 80 days and Jordan can finish the same work in 85 days, then in how many days both can finish the work together?

Correct Answer  41 ⁷/₃₃ days or 41.212 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Emma = 80 days

And, the number of days to finish the same work by Jordan = 85 days

Thus, the number of days to finish the work by Emma and Jordan together = ?

Here,

∵ In 80 days the work done by Emma = 1

∴ In 1 day, the work done by Emma = ¹/₈₀ part

Similarly,

∵ In 85 days the work done by Jordan = 1

∴ In 1 day, the work done by Jordan = ¹/₈₅ part

Now, in 1 day, the work done by Emma and Jordan together

= In 1 day work done by Emma + In 1 day the work done by Jordan

= ¹/₈₀ + ¹/₈₅

= ^{17 + 16}/₁₃₆₀

= ³³/₁₃₆₀ part of work

This means in 1 day, ³³/₁₃₆₀ part of work is done by Emma and Jordan working together.

Now, the number of days required to finish ³³/₁₃₆₀ part of work by Emma + Jordan working together = 1

∴ the number of days required to finish 1 work by Emma + Jordan together

= ¹/_³³/1360

= 1 × ¹³⁶⁰/₃₃ = ¹³⁶⁰/₃₃ days

= 41 ⁷/₃₃ days = or 41.212 days

Thus, Emma and Jordan working together will finish the work in 41 ⁷/₃₃ days = or 41.212 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 Emma = 80 days

And the number of days required to finish the same work by Jordan = 85 days

Thus, the number of days required to finish the work Emma and Jordan working together = ?

Here a = 80 days

And, b = 85 days

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

The number of days required to finish the work when Emma and Jordan working together

= ^{80 × 85}/_{80 + 85} days

= ⁶⁸⁰⁰/₁₆₅ days

= ^{6800 ÷ 5}/_{165 ÷ 5} = ¹³⁶⁰/₃₃ days

= 41 ⁷/₃₃ days or 41.212

Thus, Emma and Jordan together will finish the work in 41 ⁷/₃₃ days or 41.212 days Answer

Similar Questions

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(2) 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?

(3) Robert can finish a work in 7 days. Michael can finish the same work in 12 days while David can finish the work in 17 days. How long will it take to finish it if they work together?

(4) If Kimberly can finish the work in 38 days and Stephen can finish the same work in 43 days, then in how many days both can finish the work together?

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(6) If Emma can finish the work in 80 days and Jordan can finish the same work in 85 days, then in how many days both can finish the work together?

(7) If George can finish the work in 51 days and Dennis can finish the same work in 56 days, then in how many days both can finish the work together?

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(9) Robert can finish a work in 3 days. John can finish the same work in 4 days while Michael can finish the work in 5 days. How long will it take to finish it if they work together?

(10) Susan can finish a work in 18 days. Sarah can finish the same work in 23 days while Karen can finish the work in 28 days. How long will it take to finish it if they work together?