Time and Work
Math MCQs

Question :    If Raymond can finish the work in 97 days and Eugene can finish the same work in 102 days, then in how many days both can finish the work together?

Correct Answer  49 ¹⁴³/₁₉₉ days or 49.719 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Raymond = 97 days

And, the number of days to finish the same work by Eugene = 102 days

Thus, the number of days to finish the work by Raymond and Eugene together = ?

Here,

∵ In 97 days the work done by Raymond = 1

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

Similarly,

∵ In 102 days the work done by Eugene = 1

∴ In 1 day, the work done by Eugene = ¹/₁₀₂ part

Now, in 1 day, the work done by Raymond and Eugene together

= In 1 day work done by Raymond + In 1 day the work done by Eugene

= ¹/₉₇ + ¹/₁₀₂

= ^{102 + 97}/₉₈₉₄

= ¹⁹⁹/₉₈₉₄ part of work

This means in 1 day, ¹⁹⁹/₉₈₉₄ part of work is done by Raymond and Eugene working together.

Now, the number of days required to finish ¹⁹⁹/₉₈₉₄ part of work by Raymond + Eugene working together = 1

∴ the number of days required to finish 1 work by Raymond + Eugene together

= ¹/_{¹⁹⁹/9894}

= 1 × ⁹⁸⁹⁴/₁₉₉ = ⁹⁸⁹⁴/₁₉₉ days

= 49 ¹⁴³/₁₉₉ days = or 49.719 days

Thus, Raymond and Eugene working together will finish the work in 49 ¹⁴³/₁₉₉ days = or 49.719 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 Raymond = 97 days

And the number of days required to finish the same work by Eugene = 102 days

Thus, the number of days required to finish the work Raymond and Eugene working together = ?

Here a = 97 days

And, b = 102 days

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

The number of days required to finish the work when Raymond and Eugene working together

= ^{97 × 102}/_{97 + 102} days

= ⁹⁸⁹⁴/₁₉₉ days

= 49 ¹⁴³/₁₉₉ days or 49.719

Thus, Raymond and Eugene together will finish the work in 49 ¹⁴³/₁₉₉ days or 49.719 days Answer

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