Time and Work
Math MCQs

Question :    If Kimberly can finish the work in 35 days and Stephen can finish the same work in 38 days, then in how many days both can finish the work together?

Correct Answer  18 ¹⁶/₇₃ days or 18.219 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Kimberly = 35 days

And, the number of days to finish the same work by Stephen = 38 days

Thus, the number of days to finish the work by Kimberly and Stephen together = ?

Here,

∵ In 35 days the work done by Kimberly = 1

∴ In 1 day, the work done by Kimberly = ¹/₃₅ part

Similarly,

∵ In 38 days the work done by Stephen = 1

∴ In 1 day, the work done by Stephen = ¹/₃₈ part

Now, in 1 day, the work done by Kimberly and Stephen together

= In 1 day work done by Kimberly + In 1 day the work done by Stephen

= ¹/₃₅ + ¹/₃₈

= ^{38 + 35}/₁₃₃₀

= ⁷³/₁₃₃₀ part of work

This means in 1 day, ⁷³/₁₃₃₀ part of work is done by Kimberly and Stephen working together.

Now, the number of days required to finish ⁷³/₁₃₃₀ part of work by Kimberly + Stephen working together = 1

∴ the number of days required to finish 1 work by Kimberly + Stephen together

= ¹/_⁷³/1330

= 1 × ¹³³⁰/₇₃ = ¹³³⁰/₇₃ days

= 18 ¹⁶/₇₃ days = or 18.219 days

Thus, Kimberly and Stephen working together will finish the work in 18 ¹⁶/₇₃ days = or 18.219 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 Kimberly = 35 days

And the number of days required to finish the same work by Stephen = 38 days

Thus, the number of days required to finish the work Kimberly and Stephen working together = ?

Here a = 35 days

And, b = 38 days

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

The number of days required to finish the work when Kimberly and Stephen working together

= ^{35 × 38}/_{35 + 38} days

= ¹³³⁰/₇₃ days

= 18 ¹⁶/₇₃ days or 18.219

Thus, Kimberly and Stephen together will finish the work in 18 ¹⁶/₇₃ days or 18.219 days Answer

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