Time and Work
Math MCQs

Question :    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?

Correct Answer  47 ⁴¹/₁₈₉ days or 47.217 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Debra = 92 days

And, the number of days to finish the same work by Elijah = 97 days

Thus, the number of days to finish the work by Debra and Elijah together = ?

Here,

∵ In 92 days the work done by Debra = 1

∴ In 1 day, the work done by Debra = ¹/₉₂ part

Similarly,

∵ In 97 days the work done by Elijah = 1

∴ In 1 day, the work done by Elijah = ¹/₉₇ part

Now, in 1 day, the work done by Debra and Elijah together

= In 1 day work done by Debra + In 1 day the work done by Elijah

= ¹/₉₂ + ¹/₉₇

= ^{97 + 92}/₈₉₂₄

= ¹⁸⁹/₈₉₂₄ part of work

This means in 1 day, ¹⁸⁹/₈₉₂₄ part of work is done by Debra and Elijah working together.

Now, the number of days required to finish ¹⁸⁹/₈₉₂₄ part of work by Debra + Elijah working together = 1

∴ the number of days required to finish 1 work by Debra + Elijah together

= ¹/_{¹⁸⁹/8924}

= 1 × ⁸⁹²⁴/₁₈₉ = ⁸⁹²⁴/₁₈₉ days

= 47 ⁴¹/₁₈₉ days = or 47.217 days

Thus, Debra and Elijah working together will finish the work in 47 ⁴¹/₁₈₉ days = or 47.217 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 Debra = 92 days

And the number of days required to finish the same work by Elijah = 97 days

Thus, the number of days required to finish the work Debra and Elijah working together = ?

Here a = 92 days

And, b = 97 days

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

The number of days required to finish the work when Debra and Elijah working together

= ^{92 × 97}/_{92 + 97} days

= ⁸⁹²⁴/₁₈₉ days

= 47 ⁴¹/₁₈₉ days or 47.217

Thus, Debra and Elijah together will finish the work in 47 ⁴¹/₁₈₉ days or 47.217 days Answer

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