Time and Work
Math MCQs

Question :    If Samuel can finish the work in 87 days and Albert can finish the same work in 92 days, then in how many days both can finish the work together?

Correct Answer  44 ¹²⁸/₁₇₉ days or 44.715 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Samuel = 87 days

And, the number of days to finish the same work by Albert = 92 days

Thus, the number of days to finish the work by Samuel and Albert together = ?

Here,

∵ In 87 days the work done by Samuel = 1

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

Similarly,

∵ In 92 days the work done by Albert = 1

∴ In 1 day, the work done by Albert = ¹/₉₂ part

Now, in 1 day, the work done by Samuel and Albert together

= In 1 day work done by Samuel + In 1 day the work done by Albert

= ¹/₈₇ + ¹/₉₂

= ^{92 + 87}/₈₀₀₄

= ¹⁷⁹/₈₀₀₄ part of work

This means in 1 day, ¹⁷⁹/₈₀₀₄ part of work is done by Samuel and Albert working together.

Now, the number of days required to finish ¹⁷⁹/₈₀₀₄ part of work by Samuel + Albert working together = 1

∴ the number of days required to finish 1 work by Samuel + Albert together

= ¹/_{¹⁷⁹/8004}

= 1 × ⁸⁰⁰⁴/₁₇₉ = ⁸⁰⁰⁴/₁₇₉ days

= 44 ¹²⁸/₁₇₉ days = or 44.715 days

Thus, Samuel and Albert working together will finish the work in 44 ¹²⁸/₁₇₉ days = or 44.715 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 Samuel = 87 days

And the number of days required to finish the same work by Albert = 92 days

Thus, the number of days required to finish the work Samuel and Albert working together = ?

Here a = 87 days

And, b = 92 days

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

The number of days required to finish the work when Samuel and Albert working together

= ^{87 × 92}/_{87 + 92} days

= ⁸⁰⁰⁴/₁₇₉ days

= 44 ¹²⁸/₁₇₉ days or 44.715

Thus, Samuel and Albert together will finish the work in 44 ¹²⁸/₁₇₉ days or 44.715 days Answer

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