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) Dorothy can finish a work in 50 days. Deborah can finish the same work in 55 days while Stephanie can finish the work in 60 days. How long will it take to finish it if they work together?

(3) If Ashley can finish the work in 36 days and Eric can finish the same work in 41 days, then in how many days both can finish the work together?

(4) 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?

(5) If Linda can finish the work in 31 days and Charles can finish the same work in 47 days, then in how many days both can finish the work together?

(6) 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?

(7) If Laura can finish the work in 62 days and Kyle can finish the same work in 67 days, then in how many days both can finish the work together?

(8) If Janet can finish the work in 98 days and Russell can finish the same work in 103 days, then in how many days both can finish the work together?

(9) If Mark can finish the work in 33 days and Jacob can finish the same work in 38 days, then in how many days both can finish the work together?

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