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) If Sharon can finish the work in 60 days and Zachary can finish the same work in 65 days, then in how many days both can finish the work together?

(3) Jeffrey can finish a work in 61 days. Jacob can finish the same work in 66 days while Gary can finish the work in 71 days. How long will it take to finish it if they work together?

(4) Thomas can finish a work in 21 days. Christopher can finish the same work in 26 days while Daniel can finish the work in 31 days. How long will it take to finish it if they work together?

(5) If Anthony can finish the work in 28 days and Jeffrey can finish the same work in 32 days, then in how many days both can finish the work together?

(6) If Nancy can finish the work in 25 days and Ronald can finish the same work in 28 days, then in how many days both can finish the work together?

(7) Ronald can finish a work in 55 days. Jason can finish the same work in 60 days while Jeffrey can finish the work in 65 days. How long will it take to finish it if they work together?

(8) If Myra can finish the work in 25 days and Sophia can finish the same work in 15 days, then in how many days they both can finish the work working together?

(9) If Charles can finish the work in 20 days and Kenneth can finish the same work in 23 days, then in how many days both can finish the work together?

(10) If Annie can finish a work in 6 days and Bobby can finish the same work in 12 days, then in how many days they both can finish the work working together?