Time and Work
Math MCQs

Question :    If Paul can finish the work in 36 days and Larry can finish the same work in 40 days, then in how many days both can finish the work together?

Correct Answer  18 ¹⁸/₁₉ days or 18.947 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Paul = 36 days

And, the number of days to finish the same work by Larry = 40 days

Thus, the number of days to finish the work by Paul and Larry together = ?

Here,

∵ In 36 days the work done by Paul = 1

∴ In 1 day, the work done by Paul = ¹/₃₆ part

Similarly,

∵ In 40 days the work done by Larry = 1

∴ In 1 day, the work done by Larry = ¹/₄₀ part

Now, in 1 day, the work done by Paul and Larry together

= In 1 day work done by Paul + In 1 day the work done by Larry

= ¹/₃₆ + ¹/₄₀

= ^{10 + 9}/₃₆₀

= ¹⁹/₃₆₀ part of work

This means in 1 day, ¹⁹/₃₆₀ part of work is done by Paul and Larry working together.

Now, the number of days required to finish ¹⁹/₃₆₀ part of work by Paul + Larry working together = 1

∴ the number of days required to finish 1 work by Paul + Larry together

= ¹/_¹⁹/360

= 1 × ³⁶⁰/₁₉ = ³⁶⁰/₁₉ days

= 18 ¹⁸/₁₉ days = or 18.947 days

Thus, Paul and Larry working together will finish the work in 18 ¹⁸/₁₉ days = or 18.947 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 Paul = 36 days

And the number of days required to finish the same work by Larry = 40 days

Thus, the number of days required to finish the work Paul and Larry working together = ?

Here a = 36 days

And, b = 40 days

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

The number of days required to finish the work when Paul and Larry working together

= ^{36 × 40}/_{36 + 40} days

= ¹⁴⁴⁰/₇₆ days

= ^{1440 ÷ 4}/_{76 ÷ 4} = ³⁶⁰/₁₉ days

= 18 ¹⁸/₁₉ days or 18.947

Thus, Paul and Larry together will finish the work in 18 ¹⁸/₁₉ days or 18.947 days Answer

Similar Questions

(1) If Patricia can finish the work in 5 days and William can finish the same work in 9 days, then in how many days both can finish the work together?

(2) Katherine can finish a work in 88 days. Debra can finish the same work in 93 days while Rachel can finish the work in 98 days. How long will it take to finish it if they work together?

(3) Brian can finish a work in 49 days. Timothy can finish the same work in 54 days while Ronald can finish the work in 59 days. How long will it take to finish it if they work together?

(4) Jason can finish a work in 59 days. Ryan can finish the same work in 64 days while Jacob can finish the work in 69 days. How long will it take to finish it if they work together?

(5) If Elizabeth can finish the work in 14 days and Daniel can finish the same work in 19 days, then in how many days both can finish the work together?

(6) If Charles can finish the work in 23 days and Kenneth can finish the same work in 28 days, then in how many days both can finish the work together?

(7) If James can finish the work in 24 days and John can finish the same work in 40 days, then in how many days both can finish the work together?

(8) If A can do a piece of work in 2 days, B can do the same piece of work in 3 days, while C alone can do the same work in 4 days. Find the number of days to finish the work when they all will work together.

(9) Margaret can finish a work in 28 days. Sandra can finish the same work in 29 days while Ashley can finish the work in 30 days. How long will it take to finish it if they work together?

(10) If Mary can finish the work in 25 days and Michael can finish the same work in 41 days, then in how many days both can finish the work together?