Time and Work
Math MCQs

Question :    If Pamela can finish the work in 78 days and Dylan can finish the same work in 83 days, then in how many days both can finish the work together?

Correct Answer  40 ³⁴/₁₆₁ days or 40.211 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Pamela = 78 days

And, the number of days to finish the same work by Dylan = 83 days

Thus, the number of days to finish the work by Pamela and Dylan together = ?

Here,

∵ In 78 days the work done by Pamela = 1

∴ In 1 day, the work done by Pamela = ¹/₇₈ part

Similarly,

∵ In 83 days the work done by Dylan = 1

∴ In 1 day, the work done by Dylan = ¹/₈₃ part

Now, in 1 day, the work done by Pamela and Dylan together

= In 1 day work done by Pamela + In 1 day the work done by Dylan

= ¹/₇₈ + ¹/₈₃

= ^{83 + 78}/₆₄₇₄

= ¹⁶¹/₆₄₇₄ part of work

This means in 1 day, ¹⁶¹/₆₄₇₄ part of work is done by Pamela and Dylan working together.

Now, the number of days required to finish ¹⁶¹/₆₄₇₄ part of work by Pamela + Dylan working together = 1

∴ the number of days required to finish 1 work by Pamela + Dylan together

= ¹/_¹⁶¹/6474

= 1 × ⁶⁴⁷⁴/₁₆₁ = ⁶⁴⁷⁴/₁₆₁ days

= 40 ³⁴/₁₆₁ days = or 40.211 days

Thus, Pamela and Dylan working together will finish the work in 40 ³⁴/₁₆₁ days = or 40.211 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 Pamela = 78 days

And the number of days required to finish the same work by Dylan = 83 days

Thus, the number of days required to finish the work Pamela and Dylan working together = ?

Here a = 78 days

And, b = 83 days

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

The number of days required to finish the work when Pamela and Dylan working together

= ^{78 × 83}/_{78 + 83} days

= ⁶⁴⁷⁴/₁₆₁ days

= 40 ³⁴/₁₆₁ days or 40.211

Thus, Pamela and Dylan together will finish the work in 40 ³⁴/₁₆₁ days or 40.211 days Answer

Similar Questions

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(2) Brandon can finish a work in 83 days. Samuel can finish the same work in 88 days while Gregory can finish the work in 93 days. How long will it take to finish it if they work together?

(3) If A can do a piece of work in 2 days, B can do the same piece of work in 3 days, while C alone can do the same work in 4 days. Find the number of days to finish the work when they all will work together.

(4) If Richard can finish the work in 14 days and Mark can finish the same work in 17 days, then in how many days both can finish the work together?

(5) 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?

(6) If Michael can finish the work in 11 days and Thomas can finish the same work in 16 days, then in how many days both can finish the work together?

(7) If Ashley can finish the work in 33 days and Eric can finish the same work in 36 days, then in how many days both can finish the work together?

(8) 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?

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(10) If Nicholas can finish the work in 69 days and Roger can finish the same work in 74 days, then in how many days both can finish the work together?