Time and Work
Math MCQs

Question :    If Paul can finish the work in 36 days and Larry can finish the same work in 39 days, then in how many days both can finish the work together?

Correct Answer  18 ¹⁸/₂₅ days or 18.72 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 = 39 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 39 days the work done by Larry = 1

∴ In 1 day, the work done by Larry = ¹/₃₉ 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 + ¹/₃₉

= ^{13 + 12}/₄₆₈

= ²⁵/₄₆₈ part of work

This means in 1 day, ²⁵/₄₆₈ part of work is done by Paul and Larry working together.

Now, the number of days required to finish ²⁵/₄₆₈ part of work by Paul + Larry working together = 1

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

= ¹/_²⁵/468

= 1 × ⁴⁶⁸/₂₅ = ⁴⁶⁸/₂₅ days

= 18 ¹⁸/₂₅ days = or 18.72 days

Thus, Paul and Larry working together will finish the work in 18 ¹⁸/₂₅ days = or 18.72 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 = 39 days

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

Here a = 36 days

And, b = 39 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 × 39}/_{36 + 39} days

= ¹⁴⁰⁴/₇₅ days

= ^{1404 ÷ 3}/_{75 ÷ 3} = ⁴⁶⁸/₂₅ days

= 18 ¹⁸/₂₅ days or 18.72

Thus, Paul and Larry together will finish the work in 18 ¹⁸/₂₅ days or 18.72 days Answer

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