Time and Work
Math MCQs

Question :    If Samantha can finish the work in 86 days and Logan can finish the same work in 91 days, then in how many days both can finish the work together?

Correct Answer  44 ³⁸/₁₇₇ days or 44.215 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Samantha = 86 days

And, the number of days to finish the same work by Logan = 91 days

Thus, the number of days to finish the work by Samantha and Logan together = ?

Here,

∵ In 86 days the work done by Samantha = 1

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

Similarly,

∵ In 91 days the work done by Logan = 1

∴ In 1 day, the work done by Logan = ¹/₉₁ part

Now, in 1 day, the work done by Samantha and Logan together

= In 1 day work done by Samantha + In 1 day the work done by Logan

= ¹/₈₆ + ¹/₉₁

= ^{91 + 86}/₇₈₂₆

= ¹⁷⁷/₇₈₂₆ part of work

This means in 1 day, ¹⁷⁷/₇₈₂₆ part of work is done by Samantha and Logan working together.

Now, the number of days required to finish ¹⁷⁷/₇₈₂₆ part of work by Samantha + Logan working together = 1

∴ the number of days required to finish 1 work by Samantha + Logan together

= ¹/_{¹⁷⁷/7826}

= 1 × ⁷⁸²⁶/₁₇₇ = ⁷⁸²⁶/₁₇₇ days

= 44 ³⁸/₁₇₇ days = or 44.215 days

Thus, Samantha and Logan working together will finish the work in 44 ³⁸/₁₇₇ days = or 44.215 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 Samantha = 86 days

And the number of days required to finish the same work by Logan = 91 days

Thus, the number of days required to finish the work Samantha and Logan working together = ?

Here a = 86 days

And, b = 91 days

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

The number of days required to finish the work when Samantha and Logan working together

= ^{86 × 91}/_{86 + 91} days

= ⁷⁸²⁶/₁₇₇ days

= 44 ³⁸/₁₇₇ days or 44.215

Thus, Samantha and Logan together will finish the work in 44 ³⁸/₁₇₇ days or 44.215 days Answer

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