Time and Work
Math MCQs

Question :    If Ashley can finish the work in 33 days and Eric can finish the same work in 37 days, then in how many days both can finish the work together?

Correct Answer  17 ³¹/₇₀ days or 17.443 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Ashley = 33 days

And, the number of days to finish the same work by Eric = 37 days

Thus, the number of days to finish the work by Ashley and Eric together = ?

Here,

∵ In 33 days the work done by Ashley = 1

∴ In 1 day, the work done by Ashley = ¹/₃₃ part

Similarly,

∵ In 37 days the work done by Eric = 1

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

Now, in 1 day, the work done by Ashley and Eric together

= In 1 day work done by Ashley + In 1 day the work done by Eric

= ¹/₃₃ + ¹/₃₇

= ^{37 + 33}/₁₂₂₁

= ⁷⁰/₁₂₂₁ part of work

This means in 1 day, ⁷⁰/₁₂₂₁ part of work is done by Ashley and Eric working together.

Now, the number of days required to finish ⁷⁰/₁₂₂₁ part of work by Ashley + Eric working together = 1

∴ the number of days required to finish 1 work by Ashley + Eric together

= ¹/_⁷⁰/1221

= 1 × ¹²²¹/₇₀ = ¹²²¹/₇₀ days

= 17 ³¹/₇₀ days = or 17.443 days

Thus, Ashley and Eric working together will finish the work in 17 ³¹/₇₀ days = or 17.443 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 Ashley = 33 days

And the number of days required to finish the same work by Eric = 37 days

Thus, the number of days required to finish the work Ashley and Eric working together = ?

Here a = 33 days

And, b = 37 days

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

The number of days required to finish the work when Ashley and Eric working together

= ^{33 × 37}/_{33 + 37} days

= ¹²²¹/₇₀ days

= 17 ³¹/₇₀ days or 17.443

Thus, Ashley and Eric together will finish the work in 17 ³¹/₇₀ days or 17.443 days Answer

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