Time and Work
Math MCQs

Question :    If Patricia can finish the work in 5 days and William can finish the same work in 8 days, then in how many days both can finish the work together?

Correct Answer  3 ¹/₁₃ days or 3.077 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 = 8 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 8 days the work done by William = 1

∴ In 1 day, the work done by William = ¹/₈ 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 + ¹/₈

= ^{8 + 5}/₄₀

= ¹³/₄₀ part of work

This means in 1 day, ¹³/₄₀ part of work is done by Patricia and William working together.

Now, the number of days required to finish ¹³/₄₀ part of work by Patricia + William working together = 1

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

= ¹/_¹³/40

= 1 × ⁴⁰/₁₃ = ⁴⁰/₁₃ days

= 3 ¹/₁₃ days = or 3.077 days

Thus, Patricia and William working together will finish the work in 3 ¹/₁₃ days = or 3.077 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 = 8 days

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

Here a = 5 days

And, b = 8 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 × 8}/_{5 + 8} days

= ⁴⁰/₁₃ days

= 3 ¹/₁₃ days or 3.077

Thus, Patricia and William together will finish the work in 3 ¹/₁₃ days or 3.077 days Answer

Similar Questions

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(2) If Michael can finish the work in 30 days and Thomas can finish the same work in 46 days, then in how many days both can finish the work together?

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(7) Joshua can finish a work in 43 days. Kevin can finish the same work in 48 days while Brian can finish the work in 53 days. How long will it take to finish it if they work together?

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