Time and Work
Math MCQs

Question :    If Patrick can finish the work in 95 days and Vincent can finish the same work in 100 days, then in how many days both can finish the work together?

Correct Answer  48 ²⁸/₃₉ days or 48.718 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Patrick = 95 days

And, the number of days to finish the same work by Vincent = 100 days

Thus, the number of days to finish the work by Patrick and Vincent together = ?

Here,

∵ In 95 days the work done by Patrick = 1

∴ In 1 day, the work done by Patrick = ¹/₉₅ part

Similarly,

∵ In 100 days the work done by Vincent = 1

∴ In 1 day, the work done by Vincent = ¹/₁₀₀ part

Now, in 1 day, the work done by Patrick and Vincent together

= In 1 day work done by Patrick + In 1 day the work done by Vincent

= ¹/₉₅ + ¹/₁₀₀

= ^{20 + 19}/₁₉₀₀

= ³⁹/₁₉₀₀ part of work

This means in 1 day, ³⁹/₁₉₀₀ part of work is done by Patrick and Vincent working together.

Now, the number of days required to finish ³⁹/₁₉₀₀ part of work by Patrick + Vincent working together = 1

∴ the number of days required to finish 1 work by Patrick + Vincent together

= ¹/_³⁹/1900

= 1 × ¹⁹⁰⁰/₃₉ = ¹⁹⁰⁰/₃₉ days

= 48 ²⁸/₃₉ days = or 48.718 days

Thus, Patrick and Vincent working together will finish the work in 48 ²⁸/₃₉ days = or 48.718 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 Patrick = 95 days

And the number of days required to finish the same work by Vincent = 100 days

Thus, the number of days required to finish the work Patrick and Vincent working together = ?

Here a = 95 days

And, b = 100 days

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

The number of days required to finish the work when Patrick and Vincent working together

= ^{95 × 100}/_{95 + 100} days

= ⁹⁵⁰⁰/₁₉₅ days

= ^{9500 ÷ 5}/_{195 ÷ 5} = ¹⁹⁰⁰/₃₉ days

= 48 ²⁸/₃₉ days or 48.718

Thus, Patrick and Vincent together will finish the work in 48 ²⁸/₃₉ days or 48.718 days Answer

Similar Questions

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