Time and Work
Math MCQs

Question :    If Patricia can finish the work in 5 days and William can finish the same work in 9 days, then in how many days both can finish the work together?

Correct Answer  3 ³/₁₄ days or 3.214 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Patricia = 5 days

And, the number of days to finish the same work by William = 9 days

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

Here,

∵ In 5 days the work done by Patricia = 1

∴ In 1 day, the work done by Patricia = ¹/₅ part

Similarly,

∵ In 9 days the work done by William = 1

∴ In 1 day, the work done by William = ¹/₉ 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

= ¹/₅ + ¹/₉

= ^{9 + 5}/₄₅

= ¹⁴/₄₅ part of work

This means in 1 day, ¹⁴/₄₅ part of work is done by Patricia and William working together.

Now, the number of days required to finish ¹⁴/₄₅ part of work by Patricia + William working together = 1

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

= ¹/_¹⁴/45

= 1 × ⁴⁵/₁₄ = ⁴⁵/₁₄ days

= 3 ³/₁₄ days = or 3.214 days

Thus, Patricia and William working together will finish the work in 3 ³/₁₄ days = or 3.214 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 = 5 days

And the number of days required to finish the same work by William = 9 days

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

Here a = 5 days

And, b = 9 days

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

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

= ^{5 × 9}/_{5 + 9} days

= ⁴⁵/₁₄ days

= 3 ³/₁₄ days or 3.214

Thus, Patricia and William together will finish the work in 3 ³/₁₄ days or 3.214 days Answer

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