Time and Work
Math MCQs

Question :    If Amanda can finish the work in 45 days and Patrick can finish the same work in 48 days, then in how many days both can finish the work together?

Correct Answer  23 ⁷/₃₁ days or 23.226 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 = 48 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 48 days the work done by Patrick = 1

∴ In 1 day, the work done by Patrick = ¹/₄₈ 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 + ¹/₄₈

= ^{16 + 15}/₇₂₀

= ³¹/₇₂₀ part of work

This means in 1 day, ³¹/₇₂₀ part of work is done by Amanda and Patrick working together.

Now, the number of days required to finish ³¹/₇₂₀ part of work by Amanda + Patrick working together = 1

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

= ¹/_³¹/720

= 1 × ⁷²⁰/₃₁ = ⁷²⁰/₃₁ days

= 23 ⁷/₃₁ days = or 23.226 days

Thus, Amanda and Patrick working together will finish the work in 23 ⁷/₃₁ days = or 23.226 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 = 48 days

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

Here a = 45 days

And, b = 48 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 × 48}/_{45 + 48} days

= ²¹⁶⁰/₉₃ days

= ^{2160 ÷ 3}/_{93 ÷ 3} = ⁷²⁰/₃₁ days

= 23 ⁷/₃₁ days or 23.226

Thus, Amanda and Patrick together will finish the work in 23 ⁷/₃₁ days or 23.226 days Answer

Similar Questions

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(2) David can finish a work in 13 days. Richard can finish the same work in 18 days while Joseph can finish the work in 23 days. How long will it take to finish it if they work together?

(3) Robert can finish a work in 7 days. Michael can finish the same work in 12 days while David can finish the work in 17 days. How long will it take to finish it if they work together?

(4) If Jack can finish the work in 99 days and Bobby can finish the same work in 104 days, then in how many days both can finish the work together?

(5) If Carol can finish the work in 43 days and Alexander can finish the same work in 46 days, then in how many days both can finish the work together?

(6) If Amanda can finish the work in 45 days and Patrick can finish the same work in 48 days, then in how many days both can finish the work together?

(7) If Donna can finish the work in 42 days and Brandon can finish the same work in 47 days, then in how many days both can finish the work together?

(8) Carol can finish a work in 46 days. Dorothy can finish the same work in 51 days while Melissa can finish the work in 56 days. How long will it take to finish it if they work together?

(9) Karen can finish a work in 20 days. Lisa can finish the same work in 21 days while Nancy can finish the work in 22 days. How long will it take to finish it if they work together?

(10) If Stephen can finish the work in 75 days and Carl can finish the same work in 80 days, then in how many days both can finish the work together?