Time and Work
Math MCQs

Question :    If Amanda can finish the work in 45 days and Patrick can finish the same work in 49 days, then in how many days both can finish the work together?

Correct Answer  23 ⁴³/₉₄ days or 23.457 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Amanda = 45 days

And, the number of days to finish the same work by Patrick = 49 days

Thus, the number of days to finish the work by Amanda and Patrick together = ?

Here,

∵ In 45 days the work done by Amanda = 1

∴ In 1 day, the work done by Amanda = ¹/₄₅ part

Similarly,

∵ In 49 days the work done by Patrick = 1

∴ In 1 day, the work done by Patrick = ¹/₄₉ part

Now, in 1 day, the work done by Amanda and Patrick together

= In 1 day work done by Amanda + In 1 day the work done by Patrick

= ¹/₄₅ + ¹/₄₉

= ^{49 + 45}/₂₂₀₅

= ⁹⁴/₂₂₀₅ part of work

This means in 1 day, ⁹⁴/₂₂₀₅ part of work is done by Amanda and Patrick working together.

Now, the number of days required to finish ⁹⁴/₂₂₀₅ part of work by Amanda + Patrick working together = 1

∴ the number of days required to finish 1 work by Amanda + Patrick together

= ¹/_⁹⁴/2205

= 1 × ²²⁰⁵/₉₄ = ²²⁰⁵/₉₄ days

= 23 ⁴³/₉₄ days = or 23.457 days

Thus, Amanda and Patrick working together will finish the work in 23 ⁴³/₉₄ days = or 23.457 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 Amanda = 45 days

And the number of days required to finish the same work by Patrick = 49 days

Thus, the number of days required to finish the work Amanda and Patrick working together = ?

Here a = 45 days

And, b = 49 days

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

The number of days required to finish the work when Amanda and Patrick working together

= ^{45 × 49}/_{45 + 49} days

= ²²⁰⁵/₉₄ days

= 23 ⁴³/₉₄ days or 23.457

Thus, Amanda and Patrick together will finish the work in 23 ⁴³/₉₄ days or 23.457 days Answer

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