Time and Work
Math MCQs

Question :    If Rachel can finish the work in 94 days and Roy can finish the same work in 99 days, then in how many days both can finish the work together?

Correct Answer  48 ⁴²/₁₉₃ days or 48.218 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Rachel = 94 days

And, the number of days to finish the same work by Roy = 99 days

Thus, the number of days to finish the work by Rachel and Roy together = ?

Here,

∵ In 94 days the work done by Rachel = 1

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

Similarly,

∵ In 99 days the work done by Roy = 1

∴ In 1 day, the work done by Roy = ¹/₉₉ part

Now, in 1 day, the work done by Rachel and Roy together

= In 1 day work done by Rachel + In 1 day the work done by Roy

= ¹/₉₄ + ¹/₉₉

= ^{99 + 94}/₉₃₀₆

= ¹⁹³/₉₃₀₆ part of work

This means in 1 day, ¹⁹³/₉₃₀₆ part of work is done by Rachel and Roy working together.

Now, the number of days required to finish ¹⁹³/₉₃₀₆ part of work by Rachel + Roy working together = 1

∴ the number of days required to finish 1 work by Rachel + Roy together

= ¹/_¹⁹³/9306

= 1 × ⁹³⁰⁶/₁₉₃ = ⁹³⁰⁶/₁₉₃ days

= 48 ⁴²/₁₉₃ days = or 48.218 days

Thus, Rachel and Roy working together will finish the work in 48 ⁴²/₁₉₃ days = or 48.218 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 Rachel = 94 days

And the number of days required to finish the same work by Roy = 99 days

Thus, the number of days required to finish the work Rachel and Roy working together = ?

Here a = 94 days

And, b = 99 days

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

The number of days required to finish the work when Rachel and Roy working together

= ^{94 × 99}/_{94 + 99} days

= ⁹³⁰⁶/₁₉₃ days

= 48 ⁴²/₁₉₃ days or 48.218

Thus, Rachel and Roy together will finish the work in 48 ⁴²/₁₉₃ days or 48.218 days Answer

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