Time and Work
Math MCQs

Question :    If Ashley can finish the work in 33 days and Eric can finish the same work in 36 days, then in how many days both can finish the work together?

Correct Answer  17 ⁵/₂₃ days or 17.217 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 = 36 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 36 days the work done by Eric = 1

∴ In 1 day, the work done by Eric = ¹/₃₆ 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 + ¹/₃₆

= ^{12 + 11}/₃₉₆

= ²³/₃₉₆ part of work

This means in 1 day, ²³/₃₉₆ part of work is done by Ashley and Eric working together.

Now, the number of days required to finish ²³/₃₉₆ part of work by Ashley + Eric working together = 1

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

= ¹/_²³/396

= 1 × ³⁹⁶/₂₃ = ³⁹⁶/₂₃ days

= 17 ⁵/₂₃ days = or 17.217 days

Thus, Ashley and Eric working together will finish the work in 17 ⁵/₂₃ days = or 17.217 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 = 36 days

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

Here a = 33 days

And, b = 36 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 × 36}/_{33 + 36} days

= ¹¹⁸⁸/₆₉ days

= ^{1188 ÷ 3}/_{69 ÷ 3} = ³⁹⁶/₂₃ days

= 17 ⁵/₂₃ days or 17.217

Thus, Ashley and Eric together will finish the work in 17 ⁵/₂₃ days or 17.217 days Answer

Similar Questions

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(2) Catherine can finish a work in 100 days. Heather can finish the same work in 105 days while Diane can finish the work in 110 days. How long will it take to finish it if they work together?

(3) If Michelle can finish the work in 41 days and Samuel can finish the same work in 44 days, then in how many days both can finish the work together?

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(6) If Anthony can finish the work in 28 days and Jeffrey can finish the same work in 32 days, then in how many days both can finish the work together?

(7) If Susan can finish the work in 15 days and Donald can finish the same work in 19 days, then in how many days both can finish the work together?

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(9) If Cynthia can finish the work in 64 days and Walter can finish the same work in 69 days, then in how many days both can finish the work together?

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