Time and Work
MCQs Math


Question:     If Richard can finish the work in 36 days and Mark can finish the same work in 52 days, then in how many days both can finish the work together?


Correct Answer  21 3/11 days or 21.273 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Richard = 36 days

And, the number of days to finish the same work by Mark = 52 days

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

Here,

∵ In 36 days the work done by Richard = 1

∴ In 1 day, the work done by Richard = 1/36 part

Similarly,

∵ In 52 days the work done by Mark = 1

∴ In 1 day, the work done by Mark = 1/52 part

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

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

= 1/36 + 1/52

= 13 + 9/468

= 22/468 part of work

= 22 ÷ 2/468 ÷ 2 part of work

= 11/234 part of work

This means, in 1 day, 11/234 part of the work is done by Richard and Mark together.

Now, the number of days required to finish 11/234 part of work by Richard + Mark working together = 1

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

= 1/11/234

= 1 × 234/11 = 234/11 days

= 21 3/11 days = or 21.273 days

Thus, Richard and Mark working together will finish the work in 21 3/11 days = or 21.273 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 Richard = 36 days

And the number of days required to finish the same work by Mark = 52 days

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

Here a = 36 days

And, b = 52 days

Thus, using formula a × b/a + b days

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

= 36 × 52/36 + 52 days

= 1872/88 days

= 1872 ÷ 8/88 ÷ 8 = 234/11 days

= 21 3/11 days or 21.273

Thus, Richard and Mark together will finish the work in 21 3/11 days or 21.273 days Answer


Similar Questions

(1) 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?

(2) If Kenneth can finish the work in 42 days and Gregory can finish the same work in 46 days, then in how many days both can finish the work together?

(3) If Annie can finish a work in 6 days and Bobby can finish the same work in 12 days, then in how many days they both can finish the work working together?

(4) Margaret can finish a work in 28 days. Sandra can finish the same work in 29 days while Ashley can finish the work in 30 days. How long will it take to finish it if they work together?

(5) 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?

(6) If Lisa can finish the work in 23 days and George can finish the same work in 26 days, then in how many days both can finish the work together?

(7) If Donald can finish the work in 35 days and Nicholas can finish the same work in 40 days, then in how many days both can finish the work together?

(8) If Justin can finish the work in 79 days and Jesse can finish the same work in 84 days, then in how many days both can finish the work together?

(9) If Sandra can finish the work in 31 days and Gary can finish the same work in 34 days, then in how many days both can finish the work together?

(10) Emma can finish a work in 80 days. Helen can finish the same work in 85 days while Samantha can finish the work in 90 days. How long will it take to finish it if they work together?


NCERT Solution and CBSE Notes for class twelve, eleventh, tenth, ninth, seventh, sixth, fifth, fourth and General Math for competitive Exams. ©