Time and Work
Math MCQs

Question :    If Scott can finish the work in 81 days and Bryan can finish the same work in 86 days, then in how many days both can finish the work together?

Correct Answer  41 ¹¹⁹/₁₆₇ days or 41.713 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Scott = 81 days

And, the number of days to finish the same work by Bryan = 86 days

Thus, the number of days to finish the work by Scott and Bryan together = ?

Here,

∵ In 81 days the work done by Scott = 1

∴ In 1 day, the work done by Scott = ¹/₈₁ part

Similarly,

∵ In 86 days the work done by Bryan = 1

∴ In 1 day, the work done by Bryan = ¹/₈₆ part

Now, in 1 day, the work done by Scott and Bryan together

= In 1 day work done by Scott + In 1 day the work done by Bryan

= ¹/₈₁ + ¹/₈₆

= ^{86 + 81}/₆₉₆₆

= ¹⁶⁷/₆₉₆₆ part of work

This means in 1 day, ¹⁶⁷/₆₉₆₆ part of work is done by Scott and Bryan working together.

Now, the number of days required to finish ¹⁶⁷/₆₉₆₆ part of work by Scott + Bryan working together = 1

∴ the number of days required to finish 1 work by Scott + Bryan together

= ¹/_{¹⁶⁷/6966}

= 1 × ⁶⁹⁶⁶/₁₆₇ = ⁶⁹⁶⁶/₁₆₇ days

= 41 ¹¹⁹/₁₆₇ days = or 41.713 days

Thus, Scott and Bryan working together will finish the work in 41 ¹¹⁹/₁₆₇ days = or 41.713 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 Scott = 81 days

And the number of days required to finish the same work by Bryan = 86 days

Thus, the number of days required to finish the work Scott and Bryan working together = ?

Here a = 81 days

And, b = 86 days

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

The number of days required to finish the work when Scott and Bryan working together

= ^{81 × 86}/_{81 + 86} days

= ⁶⁹⁶⁶/₁₆₇ days

= 41 ¹¹⁹/₁₆₇ days or 41.713

Thus, Scott and Bryan together will finish the work in 41 ¹¹⁹/₁₆₇ days or 41.713 days Answer

Similar Questions

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