Time and Work
MCQs Math


Question:     If Jeffrey can finish the work in 61 days and Peter can finish the same work in 66 days, then in how many days both can finish the work together?


Correct Answer  31 89/127 days or 31.701 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Jeffrey = 61 days

And, the number of days to finish the same work by Peter = 66 days

Thus, the number of days to finish the work by Jeffrey and Peter together = ?

Here,

∵ In 61 days the work done by Jeffrey = 1

∴ In 1 day, the work done by Jeffrey = 1/61 part

Similarly,

∵ In 66 days the work done by Peter = 1

∴ In 1 day, the work done by Peter = 1/66 part

Now, in 1 day, the work done by Jeffrey and Peter together

= In 1 day work done by Jeffrey + In 1 day the work done by Peter

= 1/61 + 1/66

= 66 + 61/4026

= 127/4026 part of work

This means in 1 day, 127/4026 part of work is done by Jeffrey and Peter working together.

Now, the number of days required to finish 127/4026 part of work by Jeffrey + Peter working together = 1

∴ the number of days required to finish 1 work by Jeffrey + Peter together

= 1/127/4026

= 1 × 4026/127 = 4026/127 days

= 31 89/127 days = or 31.701 days

Thus, Jeffrey and Peter working together will finish the work in 31 89/127 days = or 31.701 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 Jeffrey = 61 days

And the number of days required to finish the same work by Peter = 66 days

Thus, the number of days required to finish the work Jeffrey and Peter working together = ?

Here a = 61 days

And, b = 66 days

Thus, using formula a × b/a + b days

The number of days required to finish the work when Jeffrey and Peter working together

= 61 × 66/61 + 66 days

= 4026/127 days

= 31 89/127 days or 31.701

Thus, Jeffrey and Peter together will finish the work in 31 89/127 days or 31.701 days Answer


Similar Questions

(1) If Nancy can finish the work in 25 days and Ronald can finish the same work in 28 days, then in how many days both can finish the work together?

(2) Carol can finish a work in 46 days. Dorothy can finish the same work in 51 days while Melissa can finish the work in 56 days. How long will it take to finish it if they work together?

(3) Michelle can finish a work in 40 days. Carol can finish the same work in 41 days while Amanda can finish the work in 42 days. How long will it take to finish it if they work together?

(4) 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?

(5) If William can finish the work in 12 days and Matthew can finish the same work in 16 days, then in how many days both can finish the work together?

(6) 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?

(7) If Jessica can finish the work in 20 days and Paul can finish the same work in 25 days, then in how many days both can finish the work together?

(8) 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?

(9) If Paul can finish the work in 39 days and Larry can finish the same work in 44 days, then in how many days both can finish the work together?

(10) If Amanda can finish the work in 48 days and Patrick can finish the same work in 53 days, then in how many days both can finish the work together?


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