Time and Work
Math MCQs

Question :    If Anthony can finish the work in 28 days and Jeffrey can finish the same work in 32 days, then in how many days both can finish the work together?

Correct Answer  14 ¹⁴/₁₅ days or 14.933 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Anthony = 28 days

And, the number of days to finish the same work by Jeffrey = 32 days

Thus, the number of days to finish the work by Anthony and Jeffrey together = ?

Here,

∵ In 28 days the work done by Anthony = 1

∴ In 1 day, the work done by Anthony = ¹/₂₈ part

Similarly,

∵ In 32 days the work done by Jeffrey = 1

∴ In 1 day, the work done by Jeffrey = ¹/₃₂ part

Now, in 1 day, the work done by Anthony and Jeffrey together

= In 1 day work done by Anthony + In 1 day the work done by Jeffrey

= ¹/₂₈ + ¹/₃₂

= ^{8 + 7}/₂₂₄

= ¹⁵/₂₂₄ part of work

This means in 1 day, ¹⁵/₂₂₄ part of work is done by Anthony and Jeffrey working together.

Now, the number of days required to finish ¹⁵/₂₂₄ part of work by Anthony + Jeffrey working together = 1

∴ the number of days required to finish 1 work by Anthony + Jeffrey together

= ¹/_¹⁵/224

= 1 × ²²⁴/₁₅ = ²²⁴/₁₅ days

= 14 ¹⁴/₁₅ days = or 14.933 days

Thus, Anthony and Jeffrey working together will finish the work in 14 ¹⁴/₁₅ days = or 14.933 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 Anthony = 28 days

And the number of days required to finish the same work by Jeffrey = 32 days

Thus, the number of days required to finish the work Anthony and Jeffrey working together = ?

Here a = 28 days

And, b = 32 days

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

The number of days required to finish the work when Anthony and Jeffrey working together

= ^{28 × 32}/_{28 + 32} days

= ⁸⁹⁶/₆₀ days

= ^{896 ÷ 4}/_{60 ÷ 4} = ²²⁴/₁₅ days

= 14 ¹⁴/₁₅ days or 14.933

Thus, Anthony and Jeffrey together will finish the work in 14 ¹⁴/₁₅ days or 14.933 days Answer

Similar Questions

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(2) Karen can finish a work in 24 days. Nancy can finish the same work in 29 days while Betty can finish the work in 34 days. How long will it take to finish it if they work together?

(3) If Debra can finish the work in 92 days and Elijah can finish the same work in 97 days, then in how many days both can finish the work together?

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(5) If Deborah can finish the work in 54 days and Aaron can finish the same work in 59 days, then in how many days both can finish the work together?

(6) If Linda can finish the work in 9 days and Charles can finish the same work in 12 days, then in how many days both can finish the work together?

(7) If Robert can finish the work in 4 days and David can finish the same work in 8 days, then in how many days both can finish the work together?

(8) William can finish a work in 11 days. Richard can finish the same work in 12 days while Joseph can finish the work in 13 days. How long will it take to finish it if they work together?

(9) 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?

(10) 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?