Time and Work
Math MCQs

Question :    If Anthony can finish the work in 31 days and Jeffrey can finish the same work in 36 days, then in how many days both can finish the work together?

Correct Answer  16 ⁴⁴/₆₇ days or 16.657 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Anthony = 31 days

And, the number of days to finish the same work by Jeffrey = 36 days

Thus, the number of days to finish the work by Anthony and Jeffrey together = ?

Here,

∵ In 31 days the work done by Anthony = 1

∴ In 1 day, the work done by Anthony = ¹/₃₁ part

Similarly,

∵ In 36 days the work done by Jeffrey = 1

∴ In 1 day, the work done by Jeffrey = ¹/₃₆ part

Now, in 1 day, the work done by Anthony and Jeffrey together

= In 1 day work done by Anthony + In 1 day the work done by Jeffrey

= ¹/₃₁ + ¹/₃₆

= ^{36 + 31}/₁₁₁₆

= ⁶⁷/₁₁₁₆ part of work

This means in 1 day, ⁶⁷/₁₁₁₆ part of work is done by Anthony and Jeffrey working together.

Now, the number of days required to finish ⁶⁷/₁₁₁₆ part of work by Anthony + Jeffrey working together = 1

∴ the number of days required to finish 1 work by Anthony + Jeffrey together

= ¹/_⁶⁷/1116

= 1 × ¹¹¹⁶/₆₇ = ¹¹¹⁶/₆₇ days

= 16 ⁴⁴/₆₇ days = or 16.657 days

Thus, Anthony and Jeffrey working together will finish the work in 16 ⁴⁴/₆₇ days = or 16.657 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 Anthony = 31 days

And the number of days required to finish the same work by Jeffrey = 36 days

Thus, the number of days required to finish the work Anthony and Jeffrey working together = ?

Here a = 31 days

And, b = 36 days

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

The number of days required to finish the work when Anthony and Jeffrey working together

= ^{31 × 36}/_{31 + 36} days

= ¹¹¹⁶/₆₇ days

= 16 ⁴⁴/₆₇ days or 16.657

Thus, Anthony and Jeffrey together will finish the work in 16 ⁴⁴/₆₇ days or 16.657 days Answer

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