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) Deborah can finish a work in 54 days. Rebecca can finish the same work in 59 days while Sharon can finish the work in 64 days. How long will it take to finish it if they work together?

(2) If George can finish the work in 48 days and Dennis can finish the same work in 51 days, then in how many days both can finish the work together?

(3) 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?

(4) If Annie can finish a work in 2 days and Bobby can finish the same work in 3 days, then in how many days they both can finish the work working together?

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(6) Donna can finish a work in 38 days. Michelle can finish the same work in 39 days while Carol can finish the work in 40 days. How long will it take to finish it if they work together?

(7) If Sandra can finish the work in 34 days and Gary can finish the same work in 39 days, then in how many days both can finish the work together?

(8) 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?

(9) If Ronald can finish the work in 55 days and Jose can finish the same work in 60 days, then in how many days both can finish the work together?

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