Time and Work
Math MCQs

Question :    If Mark can finish the work in 30 days and Jacob can finish the same work in 33 days, then in how many days both can finish the work together?

Correct Answer  15 ⁵/₇ days or 15.714 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Mark = 30 days

And, the number of days to finish the same work by Jacob = 33 days

Thus, the number of days to finish the work by Mark and Jacob together = ?

Here,

∵ In 30 days the work done by Mark = 1

∴ In 1 day, the work done by Mark = ¹/₃₀ part

Similarly,

∵ In 33 days the work done by Jacob = 1

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

Now, in 1 day, the work done by Mark and Jacob together

= In 1 day work done by Mark + In 1 day the work done by Jacob

= ¹/₃₀ + ¹/₃₃

= ^{11 + 10}/₃₃₀

= ²¹/₃₃₀ part of work

= ^{21 ÷ 3}/_{330 ÷ 3} part of work

= ⁷/₁₁₀ part of work

This means, in 1 day, ⁷/₁₁₀ part of the work is done by Mark and Jacob together.

Now, the number of days required to finish ⁷/₁₁₀ part of work by Mark + Jacob working together = 1

∴ the number of days required to finish 1 work by Mark + Jacob together

= ¹/_⁷/110

= 1 × ¹¹⁰/₇ = ¹¹⁰/₇ days

= 15 ⁵/₇ days = or 15.714 days

Thus, Mark and Jacob working together will finish the work in 15 ⁵/₇ days = or 15.714 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 Mark = 30 days

And the number of days required to finish the same work by Jacob = 33 days

Thus, the number of days required to finish the work Mark and Jacob working together = ?

Here a = 30 days

And, b = 33 days

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

The number of days required to finish the work when Mark and Jacob working together

= ^{30 × 33}/_{30 + 33} days

= ⁹⁹⁰/₆₃ days

= ^{990 ÷ 9}/_{63 ÷ 9} = ¹¹⁰/₇ days

= 15 ⁵/₇ days or 15.714

Thus, Mark and Jacob together will finish the work in 15 ⁵/₇ days or 15.714 days Answer

Similar Questions

(1) If Margaret can finish the work in 29 days and Ryan can finish the same work in 32 days, then in how many days both can finish the work together?

(2) If Matthew can finish the work in 26 days and Edward can finish the same work in 29 days, then in how many days both can finish the work together?

(3) If Steven can finish the work in 34 days and Jonathan can finish the same work in 37 days, then in how many days both can finish the work together?

(4) Joseph can finish a work in 19 days. Charles can finish the same work in 24 days while Christopher can finish the work in 29 days. How long will it take to finish it if they work together?

(5) Margaret can finish a work in 32 days. Ashley can finish the same work in 37 days while Kimberly can finish the work in 42 days. How long will it take to finish it if they work together?

(6) Kathleen can finish a work in 66 days. Angela can finish the same work in 71 days while Shirley can finish the work in 76 days. How long will it take to finish it if they work together?

(7) Emily can finish a work in 40 days. Michelle can finish the same work in 45 days while Carol can finish the work in 50 days. How long will it take to finish it if they work together?

(8) Patrick can finish a work in 95 days. Jack can finish the same work in 100 days while Dennis can finish the work in 105 days. How long will it take to finish it if they work together?

(9) If Elizabeth can finish the work in 14 days and Daniel can finish the same work in 19 days, then in how many days both can finish the work together?

(10) Sarah can finish a work in 22 days. Lisa can finish the same work in 27 days while Nancy can finish the work in 32 days. How long will it take to finish it if they work together?