Time and Work
Math MCQs

Question :    If Daniel can finish the work in 24 days and Timothy can finish the same work in 28 days, then in how many days both can finish the work together?

Correct Answer  12 ¹²/₁₃ days or 12.923 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 = 28 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 28 days the work done by Timothy = 1

∴ In 1 day, the work done by Timothy = ¹/₂₈ 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 + ¹/₂₈

= ^{7 + 6}/₁₆₈

= ¹³/₁₆₈ part of work

This means in 1 day, ¹³/₁₆₈ part of work is done by Daniel and Timothy working together.

Now, the number of days required to finish ¹³/₁₆₈ part of work by Daniel + Timothy working together = 1

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

= ¹/_¹³/168

= 1 × ¹⁶⁸/₁₃ = ¹⁶⁸/₁₃ days

= 12 ¹²/₁₃ days = or 12.923 days

Thus, Daniel and Timothy working together will finish the work in 12 ¹²/₁₃ days = or 12.923 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 = 28 days

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

Here a = 24 days

And, b = 28 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 × 28}/_{24 + 28} days

= ⁶⁷²/₅₂ days

= ^{672 ÷ 4}/_{52 ÷ 4} = ¹⁶⁸/₁₃ days

= 12 ¹²/₁₃ days or 12.923

Thus, Daniel and Timothy together will finish the work in 12 ¹²/₁₃ days or 12.923 days Answer

Similar Questions

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(2) If Linda can finish the work in 12 days and Charles can finish the same work in 17 days, then in how many days both can finish the work together?

(3) If Dorothy can finish the work in 50 days and Jack can finish the same work in 55 days, then in how many days both can finish the work together?

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(5) Jacob can finish a work in 65 days. Nicholas can finish the same work in 70 days while Eric can finish the work in 75 days. How long will it take to finish it if they work together?

(6) If Amanda can finish the work in 45 days and Patrick can finish the same work in 48 days, then in how many days both can finish the work together?

(7) If Steven can finish the work in 34 days and Jonathan can finish the same work in 38 days, then in how many days both can finish the work together?

(8) If Amy can finish the work in 68 days and Keith can finish the same work in 73 days, then in how many days both can finish the work together?

(9) 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?

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