Time and Work
Math MCQs

Question :    If Patricia can finish the work in 8 days and William can finish the same work in 13 days, then in how many days both can finish the work together?

Correct Answer  4 ²⁰/₂₁ days or 4.952 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Patricia = 8 days

And, the number of days to finish the same work by William = 13 days

Thus, the number of days to finish the work by Patricia and William together = ?

Here,

∵ In 8 days the work done by Patricia = 1

∴ In 1 day, the work done by Patricia = ¹/₈ part

Similarly,

∵ In 13 days the work done by William = 1

∴ In 1 day, the work done by William = ¹/₁₃ part

Now, in 1 day, the work done by Patricia and William together

= In 1 day work done by Patricia + In 1 day the work done by William

= ¹/₈ + ¹/₁₃

= ^{13 + 8}/₁₀₄

= ²¹/₁₀₄ part of work

This means in 1 day, ²¹/₁₀₄ part of work is done by Patricia and William working together.

Now, the number of days required to finish ²¹/₁₀₄ part of work by Patricia + William working together = 1

∴ the number of days required to finish 1 work by Patricia + William together

= ¹/_²¹/104

= 1 × ¹⁰⁴/₂₁ = ¹⁰⁴/₂₁ days

= 4 ²⁰/₂₁ days = or 4.952 days

Thus, Patricia and William working together will finish the work in 4 ²⁰/₂₁ days = or 4.952 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 Patricia = 8 days

And the number of days required to finish the same work by William = 13 days

Thus, the number of days required to finish the work Patricia and William working together = ?

Here a = 8 days

And, b = 13 days

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

The number of days required to finish the work when Patricia and William working together

= ^{8 × 13}/_{8 + 13} days

= ¹⁰⁴/₂₁ days

= 4 ²⁰/₂₁ days or 4.952

Thus, Patricia and William together will finish the work in 4 ²⁰/₂₁ days or 4.952 days Answer

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