Time and Work
Math MCQs

Question :    If Daniel can finish the work in 24 days and Timothy can finish the same work in 27 days, then in how many days both can finish the work together?

Correct Answer  12 ¹²/₁₇ days or 12.706 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Daniel = 24 days

And, the number of days to finish the same work by Timothy = 27 days

Thus, the number of days to finish the work by Daniel and Timothy together = ?

Here,

∵ In 24 days the work done by Daniel = 1

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

Similarly,

∵ In 27 days the work done by Timothy = 1

∴ In 1 day, the work done by Timothy = ¹/₂₇ part

Now, in 1 day, the work done by Daniel and Timothy together

= In 1 day work done by Daniel + In 1 day the work done by Timothy

= ¹/₂₄ + ¹/₂₇

= ^{9 + 8}/₂₁₆

= ¹⁷/₂₁₆ part of work

This means in 1 day, ¹⁷/₂₁₆ part of work is done by Daniel and Timothy working together.

Now, the number of days required to finish ¹⁷/₂₁₆ part of work by Daniel + Timothy working together = 1

∴ the number of days required to finish 1 work by Daniel + Timothy together

= ¹/_¹⁷/216

= 1 × ²¹⁶/₁₇ = ²¹⁶/₁₇ days

= 12 ¹²/₁₇ days = or 12.706 days

Thus, Daniel and Timothy working together will finish the work in 12 ¹²/₁₇ days = or 12.706 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 Daniel = 24 days

And the number of days required to finish the same work by Timothy = 27 days

Thus, the number of days required to finish the work Daniel and Timothy working together = ?

Here a = 24 days

And, b = 27 days

Thus, using formula ^{a × b}/_{a + b} days

The number of days required to finish the work when Daniel and Timothy working together

= ^{24 × 27}/_{24 + 27} days

= ⁶⁴⁸/₅₁ days

= ^{648 ÷ 3}/_{51 ÷ 3} = ²¹⁶/₁₇ days

= 12 ¹²/₁₇ days or 12.706

Thus, Daniel and Timothy together will finish the work in 12 ¹²/₁₇ days or 12.706 days Answer

Similar Questions

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(2) Ashley can finish a work in 32 days. Kimberly can finish the same work in 33 days while Emily can finish the work in 34 days. How long will it take to finish it if they work together?

(3) Timothy can finish a work in 53 days. Edward can finish the same work in 58 days while Jason can finish the work in 63 days. How long will it take to finish it if they work together?

(4) Matthew can finish a work in 29 days. Mark can finish the same work in 34 days while Donald can finish the work in 39 days. How long will it take to finish it if they work together?

(5) Betty can finish a work in 26 days. Margaret can finish the same work in 27 days while Sandra can finish the work in 28 days. How long will it take to finish it if they work together?

(6) If Larry can finish the work in 77 days and Lawrence can finish the same work in 82 days, then in how many days both can finish the work together?

(7) Melissa can finish a work in 48 days. Deborah can finish the same work in 49 days while Stephanie can finish the work in 50 days. How long will it take to finish it if they work together?

(8) If Matthew can finish the work in 26 days and Edward can finish the same work in 30 days, then in how many days both can finish the work together?

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(10) If Brian can finish the work in 46 days and Raymond can finish the same work in 49 days, then in how many days both can finish the work together?