Time and Work
Math MCQs

Question :    If Jessica can finish the work in 17 days and Paul can finish the same work in 21 days, then in how many days both can finish the work together?

Correct Answer  9 ¹⁵/₃₈ days or 9.395 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Jessica = 17 days

And, the number of days to finish the same work by Paul = 21 days

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

Here,

∵ In 17 days the work done by Jessica = 1

∴ In 1 day, the work done by Jessica = ¹/₁₇ part

Similarly,

∵ In 21 days the work done by Paul = 1

∴ In 1 day, the work done by Paul = ¹/₂₁ part

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

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

= ¹/₁₇ + ¹/₂₁

= ^{21 + 17}/₃₅₇

= ³⁸/₃₅₇ part of work

This means in 1 day, ³⁸/₃₅₇ part of work is done by Jessica and Paul working together.

Now, the number of days required to finish ³⁸/₃₅₇ part of work by Jessica + Paul working together = 1

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

= ¹/_³⁸/357

= 1 × ³⁵⁷/₃₈ = ³⁵⁷/₃₈ days

= 9 ¹⁵/₃₈ days = or 9.395 days

Thus, Jessica and Paul working together will finish the work in 9 ¹⁵/₃₈ days = or 9.395 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 Jessica = 17 days

And the number of days required to finish the same work by Paul = 21 days

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

Here a = 17 days

And, b = 21 days

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

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

= ^{17 × 21}/_{17 + 21} days

= ³⁵⁷/₃₈ days

= 9 ¹⁵/₃₈ days or 9.395

Thus, Jessica and Paul together will finish the work in 9 ¹⁵/₃₈ days or 9.395 days Answer

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