Time and Work
Math MCQs

Question :    If Melissa can finish the work in 49 days and Jerry can finish the same work in 52 days, then in how many days both can finish the work together?

Correct Answer  25 ²³/₁₀₁ days or 25.228 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Melissa = 49 days

And, the number of days to finish the same work by Jerry = 52 days

Thus, the number of days to finish the work by Melissa and Jerry together = ?

Here,

∵ In 49 days the work done by Melissa = 1

∴ In 1 day, the work done by Melissa = ¹/₄₉ part

Similarly,

∵ In 52 days the work done by Jerry = 1

∴ In 1 day, the work done by Jerry = ¹/₅₂ part

Now, in 1 day, the work done by Melissa and Jerry together

= In 1 day work done by Melissa + In 1 day the work done by Jerry

= ¹/₄₉ + ¹/₅₂

= ^{52 + 49}/₂₅₄₈

= ¹⁰¹/₂₅₄₈ part of work

This means in 1 day, ¹⁰¹/₂₅₄₈ part of work is done by Melissa and Jerry working together.

Now, the number of days required to finish ¹⁰¹/₂₅₄₈ part of work by Melissa + Jerry working together = 1

∴ the number of days required to finish 1 work by Melissa + Jerry together

= ¹/_¹⁰¹/2548

= 1 × ²⁵⁴⁸/₁₀₁ = ²⁵⁴⁸/₁₀₁ days

= 25 ²³/₁₀₁ days = or 25.228 days

Thus, Melissa and Jerry working together will finish the work in 25 ²³/₁₀₁ days = or 25.228 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 Melissa = 49 days

And the number of days required to finish the same work by Jerry = 52 days

Thus, the number of days required to finish the work Melissa and Jerry working together = ?

Here a = 49 days

And, b = 52 days

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

The number of days required to finish the work when Melissa and Jerry working together

= ^{49 × 52}/_{49 + 52} days

= ²⁵⁴⁸/₁₀₁ days

= 25 ²³/₁₀₁ days or 25.228

Thus, Melissa and Jerry together will finish the work in 25 ²³/₁₀₁ days or 25.228 days Answer

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