Time and Work
Math MCQs

Question :    If Matthew can finish the work in 26 days and Edward can finish the same work in 29 days, then in how many days both can finish the work together?

Correct Answer  13 ³⁹/₅₅ days or 13.709 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Matthew = 26 days

And, the number of days to finish the same work by Edward = 29 days

Thus, the number of days to finish the work by Matthew and Edward together = ?

Here,

∵ In 26 days the work done by Matthew = 1

∴ In 1 day, the work done by Matthew = ¹/₂₆ part

Similarly,

∵ In 29 days the work done by Edward = 1

∴ In 1 day, the work done by Edward = ¹/₂₉ part

Now, in 1 day, the work done by Matthew and Edward together

= In 1 day work done by Matthew + In 1 day the work done by Edward

= ¹/₂₆ + ¹/₂₉

= ^{29 + 26}/₇₅₄

= ⁵⁵/₇₅₄ part of work

This means in 1 day, ⁵⁵/₇₅₄ part of work is done by Matthew and Edward working together.

Now, the number of days required to finish ⁵⁵/₇₅₄ part of work by Matthew + Edward working together = 1

∴ the number of days required to finish 1 work by Matthew + Edward together

= ¹/_⁵⁵/754

= 1 × ⁷⁵⁴/₅₅ = ⁷⁵⁴/₅₅ days

= 13 ³⁹/₅₅ days = or 13.709 days

Thus, Matthew and Edward working together will finish the work in 13 ³⁹/₅₅ days = or 13.709 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 Matthew = 26 days

And the number of days required to finish the same work by Edward = 29 days

Thus, the number of days required to finish the work Matthew and Edward working together = ?

Here a = 26 days

And, b = 29 days

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

The number of days required to finish the work when Matthew and Edward working together

= ^{26 × 29}/_{26 + 29} days

= ⁷⁵⁴/₅₅ days

= 13 ³⁹/₅₅ days or 13.709

Thus, Matthew and Edward together will finish the work in 13 ³⁹/₅₅ days or 13.709 days Answer

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