Time and Work
Math MCQs

Question :    If Gregory can finish the work in 89 days and Alan can finish the same work in 94 days, then in how many days both can finish the work together?

Correct Answer  45 ¹³¹/₁₈₃ days or 45.716 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Gregory = 89 days

And, the number of days to finish the same work by Alan = 94 days

Thus, the number of days to finish the work by Gregory and Alan together = ?

Here,

∵ In 89 days the work done by Gregory = 1

∴ In 1 day, the work done by Gregory = ¹/₈₉ part

Similarly,

∵ In 94 days the work done by Alan = 1

∴ In 1 day, the work done by Alan = ¹/₉₄ part

Now, in 1 day, the work done by Gregory and Alan together

= In 1 day work done by Gregory + In 1 day the work done by Alan

= ¹/₈₉ + ¹/₉₄

= ^{94 + 89}/₈₃₆₆

= ¹⁸³/₈₃₆₆ part of work

This means in 1 day, ¹⁸³/₈₃₆₆ part of work is done by Gregory and Alan working together.

Now, the number of days required to finish ¹⁸³/₈₃₆₆ part of work by Gregory + Alan working together = 1

∴ the number of days required to finish 1 work by Gregory + Alan together

= ¹/_¹⁸³/8366

= 1 × ⁸³⁶⁶/₁₈₃ = ⁸³⁶⁶/₁₈₃ days

= 45 ¹³¹/₁₈₃ days = or 45.716 days

Thus, Gregory and Alan working together will finish the work in 45 ¹³¹/₁₈₃ days = or 45.716 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 Gregory = 89 days

And the number of days required to finish the same work by Alan = 94 days

Thus, the number of days required to finish the work Gregory and Alan working together = ?

Here a = 89 days

And, b = 94 days

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

The number of days required to finish the work when Gregory and Alan working together

= ^{89 × 94}/_{89 + 94} days

= ⁸³⁶⁶/₁₈₃ days

= 45 ¹³¹/₁₈₃ days or 45.716

Thus, Gregory and Alan together will finish the work in 45 ¹³¹/₁₈₃ days or 45.716 days Answer

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