Time and Work
MCQs Math


Question:     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?


Correct Answer  18 12/73 days or 18.164 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Sandra = 34 days

And, the number of days to finish the same work by Gary = 39 days

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

Here,

∵ In 34 days the work done by Sandra = 1

∴ In 1 day, the work done by Sandra = 1/34 part

Similarly,

∵ In 39 days the work done by Gary = 1

∴ In 1 day, the work done by Gary = 1/39 part

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

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

= 1/34 + 1/39

= 39 + 34/1326

= 73/1326 part of work

This means in 1 day, 73/1326 part of work is done by Sandra and Gary working together.

Now, the number of days required to finish 73/1326 part of work by Sandra + Gary working together = 1

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

= 1/73/1326

= 1 × 1326/73 = 1326/73 days

= 18 12/73 days = or 18.164 days

Thus, Sandra and Gary working together will finish the work in 18 12/73 days = or 18.164 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 Sandra = 34 days

And the number of days required to finish the same work by Gary = 39 days

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

Here a = 34 days

And, b = 39 days

Thus, using formula a × b/a + b days

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

= 34 × 39/34 + 39 days

= 1326/73 days

= 18 12/73 days or 18.164

Thus, Sandra and Gary together will finish the work in 18 12/73 days or 18.164 days Answer


Similar Questions

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(2) If Thomas can finish the work in 21 days and Andrew can finish the same work in 26 days, then in how many days both can finish the work together?

(3) If Carolyn can finish the work in 96 days and Ralph can finish the same work in 101 days, then in how many days both can finish the work together?

(4) Ryan can finish a work in 63 days. Gary can finish the same work in 68 days while Nicholas can finish the work in 73 days. How long will it take to finish it if they work together?

(5) If Robert can finish a work in 5 days and Bob can finish the same work in 6 days, then in how many days they both can finish the work working together?

(6) If Brandon can finish the work in 83 days and Joe can finish the same work in 88 days, then in how many days both can finish the work together?

(7) Debra can finish a work in 92 days. Carolyn can finish the same work in 97 days while Janet can finish the work in 102 days. How long will it take to finish it if they work together?

(8) If Brian can finish the work in 46 days and Raymond can finish the same work in 50 days, then in how many days both can finish the work together?

(9) Steven can finish a work in 37 days. Andrew can finish the same work in 42 days while Joshua can finish the work in 47 days. How long will it take to finish it if they work together?

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