Time and Work
MCQs Math


Question:     If John can finish the work in 28 days and Richard can finish the same work in 44 days, then in how many days both can finish the work together?


Correct Answer  17 1/9 days or 17.111 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by John = 28 days

And, the number of days to finish the same work by Richard = 44 days

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

Here,

∵ In 28 days the work done by John = 1

∴ In 1 day, the work done by John = 1/28 part

Similarly,

∵ In 44 days the work done by Richard = 1

∴ In 1 day, the work done by Richard = 1/44 part

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

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

= 1/28 + 1/44

= 11 + 7/308

= 18/308 part of work

= 18 ÷ 2/308 ÷ 2 part of work

= 9/154 part of work

This means, in 1 day, 9/154 part of the work is done by John and Richard together.

Now, the number of days required to finish 9/154 part of work by John + Richard working together = 1

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

= 1/9/154

= 1 × 154/9 = 154/9 days

= 17 1/9 days = or 17.111 days

Thus, John and Richard working together will finish the work in 17 1/9 days = or 17.111 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 John = 28 days

And the number of days required to finish the same work by Richard = 44 days

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

Here a = 28 days

And, b = 44 days

Thus, using formula a × b/a + b days

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

= 28 × 44/28 + 44 days

= 1232/72 days

= 1232 ÷ 8/72 ÷ 8 = 154/9 days

= 17 1/9 days or 17.111

Thus, John and Richard together will finish the work in 17 1/9 days or 17.111 days Answer


Similar Questions

(1) If Karen can finish the work in 24 days and Kevin can finish the same work in 29 days, then in how many days both can finish the work together?

(2) If Karen can finish the work in 21 days and Kevin can finish the same work in 24 days, then in how many days both can finish the work together?

(3) Kimberly can finish a work in 34 days. Emily can finish the same work in 35 days while Donna can finish the work in 36 days. How long will it take to finish it if they work together?

(4) If Mark can finish the work in 30 days and Jacob can finish the same work in 34 days, then in how many days both can finish the work together?

(5) David can finish a work in 13 days. Richard can finish the same work in 18 days while Joseph can finish the work in 23 days. How long will it take to finish it if they work together?

(6) If Linda can finish the work in 9 days and Charles can finish the same work in 13 days, then in how many days both can finish the work together?

(7) If Carol can finish the work in 43 days and Alexander can finish the same work in 46 days, then in how many days both can finish the work together?

(8) If Elizabeth can finish the work in 11 days and Daniel can finish the same work in 15 days, then in how many days both can finish the work together?

(9) If Kimberly can finish the work in 35 days and Stephen can finish the same work in 39 days, then in how many days both can finish the work together?

(10) Betty can finish a work in 30 days. Sandra can finish the same work in 35 days while Ashley can finish the work in 40 days. How long will it take to finish it if they work together?


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