Time and Work
MCQs Math


Question:     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?


Correct Answer  11 1/5 days or 11.2 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Karen = 21 days

And, the number of days to finish the same work by Kevin = 24 days

Thus, the number of days to finish the work by Karen and Kevin together = ?

Here,

∵ In 21 days the work done by Karen = 1

∴ In 1 day, the work done by Karen = 1/21 part

Similarly,

∵ In 24 days the work done by Kevin = 1

∴ In 1 day, the work done by Kevin = 1/24 part

Now, in 1 day, the work done by Karen and Kevin together

= In 1 day work done by Karen + In 1 day the work done by Kevin

= 1/21 + 1/24

= 8 + 7/168

= 15/168 part of work

= 15 ÷ 3/168 ÷ 3 part of work

= 5/56 part of work

This means, in 1 day, 5/56 part of the work is done by Karen and Kevin together.

Now, the number of days required to finish 5/56 part of work by Karen + Kevin working together = 1

∴ the number of days required to finish 1 work by Karen + Kevin together

= 1/5/56

= 1 × 56/5 = 56/5 days

= 11 1/5 days = or 11.2 days

Thus, Karen and Kevin working together will finish the work in 11 1/5 days = or 11.2 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 Karen = 21 days

And the number of days required to finish the same work by Kevin = 24 days

Thus, the number of days required to finish the work Karen and Kevin working together = ?

Here a = 21 days

And, b = 24 days

Thus, using formula a × b/a + b days

The number of days required to finish the work when Karen and Kevin working together

= 21 × 24/21 + 24 days

= 504/45 days

= 504 ÷ 9/45 ÷ 9 = 56/5 days

= 11 1/5 days or 11.2

Thus, Karen and Kevin together will finish the work in 11 1/5 days or 11.2 days Answer


Similar Questions

(1) If David can finish the work in 10 days and Christopher can finish the same work in 13 days, then in how many days both can finish the work together?

(2) 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?

(3) If Ashley can finish the work in 36 days and Eric can finish the same work in 41 days, then in how many days both can finish the work together?

(4) If Anthony can finish the work in 28 days and Jeffrey can finish the same work in 31 days, then in how many days both can finish the work together?

(5) Amanda can finish a work in 48 days. Melissa can finish the same work in 53 days while Deborah can finish the work in 58 days. How long will it take to finish it if they work together?

(6) If William can finish the work in 34 days and Matthew can finish the same work in 50 days, then in how many days both can finish the work together?

(7) Deborah can finish a work in 50 days. Stephanie can finish the same work in 51 days while Rebecca can finish the work in 52 days. How long will it take to finish it if they work together?

(8) If Patricia can finish the work in 27 days and William can finish the same work in 43 days, then in how many days both can finish the work together?

(9) Andrew can finish a work in 41 days. Kenneth can finish the same work in 46 days while Kevin can finish the work in 51 days. How long will it take to finish it if they work together?

(10) Anthony can finish a work in 27 days. Mark can finish the same work in 28 days while Donald can finish the work in 29 days. How long will it take to finish it if they work together?


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