Time and Work
MCQs Math


Question:     If Gary can finish the work in 67 days and Christian can finish the same work in 72 days, then in how many days both can finish the work together?


Correct Answer  34 98/139 days or 34.705 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Gary = 67 days

And, the number of days to finish the same work by Christian = 72 days

Thus, the number of days to finish the work by Gary and Christian together = ?

Here,

∵ In 67 days the work done by Gary = 1

∴ In 1 day, the work done by Gary = 1/67 part

Similarly,

∵ In 72 days the work done by Christian = 1

∴ In 1 day, the work done by Christian = 1/72 part

Now, in 1 day, the work done by Gary and Christian together

= In 1 day work done by Gary + In 1 day the work done by Christian

= 1/67 + 1/72

= 72 + 67/4824

= 139/4824 part of work

This means in 1 day, 139/4824 part of work is done by Gary and Christian working together.

Now, the number of days required to finish 139/4824 part of work by Gary + Christian working together = 1

∴ the number of days required to finish 1 work by Gary + Christian together

= 1/139/4824

= 1 × 4824/139 = 4824/139 days

= 34 98/139 days = or 34.705 days

Thus, Gary and Christian working together will finish the work in 34 98/139 days = or 34.705 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 Gary = 67 days

And the number of days required to finish the same work by Christian = 72 days

Thus, the number of days required to finish the work Gary and Christian working together = ?

Here a = 67 days

And, b = 72 days

Thus, using formula a × b/a + b days

The number of days required to finish the work when Gary and Christian working together

= 67 × 72/67 + 72 days

= 4824/139 days

= 34 98/139 days or 34.705

Thus, Gary and Christian together will finish the work in 34 98/139 days or 34.705 days Answer


Similar Questions

(1) If Margaret can finish the work in 29 days and Ryan can finish the same work in 33 days, then in how many days both can finish the work together?

(2) Jonathan can finish a work in 73 days. Larry can finish the same work in 78 days while Justin can finish the work in 83 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 45 days, then in how many days both can finish the work together?

(4) If Raymond can finish the work in 97 days and Eugene can finish the same work in 102 days, then in how many days both can finish the work together?

(5) George can finish a work in 51 days. Ronald can finish the same work in 56 days while Edward can finish the work in 61 days. How long will it take to finish it if they work together?

(6) Samantha can finish a work in 86 days. Christine can finish the same work in 91 days while Debra can finish the work in 96 days. How long will it take to finish it if they work together?

(7) Richard can finish a work in 17 days. Thomas can finish the same work in 22 days while Charles can finish the work in 27 days. How long will it take to finish it if they work together?

(8) Shirley can finish a work in 72 days. Brenda can finish the same work in 77 days while Pamela can finish the work in 82 days. How long will it take to finish it if they work together?

(9) 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?

(10) Christopher can finish a work in 21 days. Daniel can finish the same work in 22 days while Matthew can finish the work in 23 days. How long will it take to finish it if they work together?


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