Time and Work
Math MCQs

Question :    If Dorothy can finish the work in 47 days and Jack can finish the same work in 50 days, then in how many days both can finish the work together?

Correct Answer  24 ²²/₉₇ days or 24.227 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Dorothy = 47 days

And, the number of days to finish the same work by Jack = 50 days

Thus, the number of days to finish the work by Dorothy and Jack together = ?

Here,

∵ In 47 days the work done by Dorothy = 1

∴ In 1 day, the work done by Dorothy = ¹/₄₇ part

Similarly,

∵ In 50 days the work done by Jack = 1

∴ In 1 day, the work done by Jack = ¹/₅₀ part

Now, in 1 day, the work done by Dorothy and Jack together

= In 1 day work done by Dorothy + In 1 day the work done by Jack

= ¹/₄₇ + ¹/₅₀

= ^{50 + 47}/₂₃₅₀

= ⁹⁷/₂₃₅₀ part of work

This means in 1 day, ⁹⁷/₂₃₅₀ part of work is done by Dorothy and Jack working together.

Now, the number of days required to finish ⁹⁷/₂₃₅₀ part of work by Dorothy + Jack working together = 1

∴ the number of days required to finish 1 work by Dorothy + Jack together

= ¹/_⁹⁷/2350

= 1 × ²³⁵⁰/₉₇ = ²³⁵⁰/₉₇ days

= 24 ²²/₉₇ days = or 24.227 days

Thus, Dorothy and Jack working together will finish the work in 24 ²²/₉₇ days = or 24.227 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 Dorothy = 47 days

And the number of days required to finish the same work by Jack = 50 days

Thus, the number of days required to finish the work Dorothy and Jack working together = ?

Here a = 47 days

And, b = 50 days

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

The number of days required to finish the work when Dorothy and Jack working together

= ^{47 × 50}/_{47 + 50} days

= ²³⁵⁰/₉₇ days

= 24 ²²/₉₇ days or 24.227

Thus, Dorothy and Jack together will finish the work in 24 ²²/₉₇ days or 24.227 days Answer

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