Time and Work
MCQs Math


Question:     If Richard can finish the work in 17 days and Mark can finish the same work in 22 days, then in how many days both can finish the work together?


Correct Answer  9 23/39 days or 9.59 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Richard = 17 days

And, the number of days to finish the same work by Mark = 22 days

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

Here,

∵ In 17 days the work done by Richard = 1

∴ In 1 day, the work done by Richard = 1/17 part

Similarly,

∵ In 22 days the work done by Mark = 1

∴ In 1 day, the work done by Mark = 1/22 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

= 1/17 + 1/22

= 22 + 17/374

= 39/374 part of work

This means in 1 day, 39/374 part of work is done by Richard and Mark working together.

Now, the number of days required to finish 39/374 part of work by Richard + Mark working together = 1

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

= 1/39/374

= 1 × 374/39 = 374/39 days

= 9 23/39 days = or 9.59 days

Thus, Richard and Mark working together will finish the work in 9 23/39 days = or 9.59 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 = 17 days

And the number of days required to finish the same work by Mark = 22 days

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

Here a = 17 days

And, b = 22 days

Thus, using formula a × b/a + b days

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

= 17 × 22/17 + 22 days

= 374/39 days

= 9 23/39 days or 9.59

Thus, Richard and Mark together will finish the work in 9 23/39 days or 9.59 days Answer


Similar Questions

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(2) Paul can finish a work in 35 days. Andrew can finish the same work in 36 days while Joshua can finish the work in 37 days. How long will it take to finish it if they work together?

(3) If James can finish the work in 2 days and John can finish the same work in 6 days, then in how many days both can finish the work together?

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(6) Timothy can finish a work in 49 days. Ronald can finish the same work in 50 days while Edward can finish the work in 51 days. How long will it take to finish it if they work together?

(7) If Robert can finish the work in 4 days and David can finish the same work in 8 days, then in how many days both can finish the work together?

(8) 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?

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