Time and Work
Math MCQs

Question :    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?

Correct Answer  28 ²²/₁₁₃ days or 28.195 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Deborah = 54 days

And, the number of days to finish the same work by Aaron = 59 days

Thus, the number of days to finish the work by Deborah and Aaron together = ?

Here,

∵ In 54 days the work done by Deborah = 1

∴ In 1 day, the work done by Deborah = ¹/₅₄ part

Similarly,

∵ In 59 days the work done by Aaron = 1

∴ In 1 day, the work done by Aaron = ¹/₅₉ part

Now, in 1 day, the work done by Deborah and Aaron together

= In 1 day work done by Deborah + In 1 day the work done by Aaron

= ¹/₅₄ + ¹/₅₉

= ^{59 + 54}/₃₁₈₆

= ¹¹³/₃₁₈₆ part of work

This means in 1 day, ¹¹³/₃₁₈₆ part of work is done by Deborah and Aaron working together.

Now, the number of days required to finish ¹¹³/₃₁₈₆ part of work by Deborah + Aaron working together = 1

∴ the number of days required to finish 1 work by Deborah + Aaron together

= ¹/_¹¹³/3186

= 1 × ³¹⁸⁶/₁₁₃ = ³¹⁸⁶/₁₁₃ days

= 28 ²²/₁₁₃ days = or 28.195 days

Thus, Deborah and Aaron working together will finish the work in 28 ²²/₁₁₃ days = or 28.195 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 Deborah = 54 days

And the number of days required to finish the same work by Aaron = 59 days

Thus, the number of days required to finish the work Deborah and Aaron working together = ?

Here a = 54 days

And, b = 59 days

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

The number of days required to finish the work when Deborah and Aaron working together

= ^{54 × 59}/_{54 + 59} days

= ³¹⁸⁶/₁₁₃ days

= 28 ²²/₁₁₃ days or 28.195

Thus, Deborah and Aaron together will finish the work in 28 ²²/₁₁₃ days or 28.195 days Answer

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