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

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(3) If Betty can finish the work in 27 days and Jason can finish the same work in 31 days, then in how many days both can finish the work together?

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(6) If Annie can finish a work in 5 days and Bobby can finish the same work in 10 days, then in how many days they both can finish the work working together?

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(8) If Margaret can finish the work in 29 days and Ryan can finish the same work in 32 days, then in how many days both can finish the work together?

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