Time and Work
Math MCQs

Question :    If Emily can finish the work in 37 days and Justin can finish the same work in 40 days, then in how many days both can finish the work together?

Correct Answer  19 ¹⁷/₇₇ days or 19.221 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Emily = 37 days

And, the number of days to finish the same work by Justin = 40 days

Thus, the number of days to finish the work by Emily and Justin together = ?

Here,

∵ In 37 days the work done by Emily = 1

∴ In 1 day, the work done by Emily = ¹/₃₇ part

Similarly,

∵ In 40 days the work done by Justin = 1

∴ In 1 day, the work done by Justin = ¹/₄₀ part

Now, in 1 day, the work done by Emily and Justin together

= In 1 day work done by Emily + In 1 day the work done by Justin

= ¹/₃₇ + ¹/₄₀

= ^{40 + 37}/₁₄₈₀

= ⁷⁷/₁₄₈₀ part of work

This means in 1 day, ⁷⁷/₁₄₈₀ part of work is done by Emily and Justin working together.

Now, the number of days required to finish ⁷⁷/₁₄₈₀ part of work by Emily + Justin working together = 1

∴ the number of days required to finish 1 work by Emily + Justin together

= ¹/_⁷⁷/1480

= 1 × ¹⁴⁸⁰/₇₇ = ¹⁴⁸⁰/₇₇ days

= 19 ¹⁷/₇₇ days = or 19.221 days

Thus, Emily and Justin working together will finish the work in 19 ¹⁷/₇₇ days = or 19.221 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 Emily = 37 days

And the number of days required to finish the same work by Justin = 40 days

Thus, the number of days required to finish the work Emily and Justin working together = ?

Here a = 37 days

And, b = 40 days

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

The number of days required to finish the work when Emily and Justin working together

= ^{37 × 40}/_{37 + 40} days

= ¹⁴⁸⁰/₇₇ days

= 19 ¹⁷/₇₇ days or 19.221

Thus, Emily and Justin together will finish the work in 19 ¹⁷/₇₇ days or 19.221 days Answer

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