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

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(2) If A can finish a work in 10 days and B can finish the same work in 15 days, then in how many days they both can finish the work working together?

(3) If Frank can finish the work in 93 days and Randy can finish the same work in 98 days, then in how many days both can finish the work together?

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(6) 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?

(7) If Thomas can finish the work in 18 days and Andrew can finish the same work in 22 days, then in how many days both can finish the work together?

(8) 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?

(9) If Rebecca can finish the work in 58 days and Henry can finish the same work in 63 days, then in how many days both can finish the work together?

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