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

(1) If Matthew can finish the work in 29 days and Edward can finish the same work in 34 days, then in how many days both can finish the work together?

(2) Karen can finish a work in 20 days. Lisa can finish the same work in 21 days while Nancy can finish the work in 22 days. How long will it take to finish it if they work together?

(3) If Sarah can finish the work in 22 days and Joshua can finish the same work in 27 days, then in how many days both can finish the work together?

(4) If Michelle can finish the work in 41 days and Samuel can finish the same work in 45 days, then in how many days both can finish the work together?

(5) Matthew can finish a work in 25 days. Anthony can finish the same work in 26 days while Mark can finish the work in 27 days. How long will it take to finish it if they work together?

(6) If Jack can finish the work in 20 days and Bill can finish the same work in 30 days, then in how many days they both can finish the work working together?

(7) James can finish a work in 5 days. John can finish the same work in 10 days while Michael can finish the work in 15 days. How long will it take to finish it if they work together?

(8) If Matthew can finish the work in 26 days and Edward can finish the same work in 30 days, then in how many days both can finish the work together?

(9) If Steven can finish the work in 34 days and Jonathan can finish the same work in 38 days, then in how many days both can finish the work together?

(10) Donald can finish a work in 35 days. Paul can finish the same work in 40 days while Andrew can finish the work in 45 days. How long will it take to finish it if they work together?