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

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