Time and Work
Math MCQs

Question :    If Nicole can finish the work in 82 days and Billy can finish the same work in 87 days, then in how many days both can finish the work together?

Correct Answer  42 ³⁶/₁₆₉ days or 42.213 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Nicole = 82 days

And, the number of days to finish the same work by Billy = 87 days

Thus, the number of days to finish the work by Nicole and Billy together = ?

Here,

∵ In 82 days the work done by Nicole = 1

∴ In 1 day, the work done by Nicole = ¹/₈₂ part

Similarly,

∵ In 87 days the work done by Billy = 1

∴ In 1 day, the work done by Billy = ¹/₈₇ part

Now, in 1 day, the work done by Nicole and Billy together

= In 1 day work done by Nicole + In 1 day the work done by Billy

= ¹/₈₂ + ¹/₈₇

= ^{87 + 82}/₇₁₃₄

= ¹⁶⁹/₇₁₃₄ part of work

This means in 1 day, ¹⁶⁹/₇₁₃₄ part of work is done by Nicole and Billy working together.

Now, the number of days required to finish ¹⁶⁹/₇₁₃₄ part of work by Nicole + Billy working together = 1

∴ the number of days required to finish 1 work by Nicole + Billy together

= ¹/_{¹⁶⁹/7134}

= 1 × ⁷¹³⁴/₁₆₉ = ⁷¹³⁴/₁₆₉ days

= 42 ³⁶/₁₆₉ days = or 42.213 days

Thus, Nicole and Billy working together will finish the work in 42 ³⁶/₁₆₉ days = or 42.213 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 Nicole = 82 days

And the number of days required to finish the same work by Billy = 87 days

Thus, the number of days required to finish the work Nicole and Billy working together = ?

Here a = 82 days

And, b = 87 days

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

The number of days required to finish the work when Nicole and Billy working together

= ^{82 × 87}/_{82 + 87} days

= ⁷¹³⁴/₁₆₉ days

= 42 ³⁶/₁₆₉ days or 42.213

Thus, Nicole and Billy together will finish the work in 42 ³⁶/₁₆₉ days or 42.213 days Answer

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