Time and Work
Math MCQs

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 & 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 Susan can finish the work in 18 days and Donald can finish the same work in 23 days, then in how many days both can finish the work together?

(2) 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?

(3) If Brenda can finish the work in 76 days and Arthur can finish the same work in 81 days, then in how many days both can finish the work together?

(4) Elizabeth can finish a work in 14 days. Susan can finish the same work in 19 days while Jessica can finish the work in 24 days. How long will it take to finish it if they work together?

(5) 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?

(6) Scott can finish a work in 81 days. Benjamin can finish the same work in 86 days while Samuel can finish the work in 91 days. How long will it take to finish it if they work together?

(7) Sandra can finish a work in 34 days. Kimberly can finish the same work in 39 days while Emily can finish the work in 44 days. How long will it take to finish it if they work together?

(8) Joshua can finish a work in 43 days. Kevin can finish the same work in 48 days while Brian can finish the work in 53 days. How long will it take to finish it if they work together?

(9) If Donald can finish the work in 32 days and Nicholas can finish the same work in 36 days, then in how many days both can finish the work together?

(10) 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?