Time and Work
Math MCQs

Question :    If Patricia can finish the work in 27 days and William can finish the same work in 43 days, then in how many days both can finish the work together?

Correct Answer  16 ⁴¹/₇₀ days or 16.586 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Patricia = 27 days

And, the number of days to finish the same work by William = 43 days

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

Here,

∵ In 27 days the work done by Patricia = 1

∴ In 1 day, the work done by Patricia = ¹/₂₇ part

Similarly,

∵ In 43 days the work done by William = 1

∴ In 1 day, the work done by William = ¹/₄₃ 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

= ¹/₂₇ + ¹/₄₃

= ^{43 + 27}/₁₁₆₁

= ⁷⁰/₁₁₆₁ part of work

This means in 1 day, ⁷⁰/₁₁₆₁ part of work is done by Patricia and William working together.

Now, the number of days required to finish ⁷⁰/₁₁₆₁ part of work by Patricia + William working together = 1

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

= ¹/_⁷⁰/1161

= 1 × ¹¹⁶¹/₇₀ = ¹¹⁶¹/₇₀ days

= 16 ⁴¹/₇₀ days = or 16.586 days

Thus, Patricia and William working together will finish the work in 16 ⁴¹/₇₀ days = or 16.586 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 = 27 days

And the number of days required to finish the same work by William = 43 days

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

Here a = 27 days

And, b = 43 days

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

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

= ^{27 × 43}/_{27 + 43} days

= ¹¹⁶¹/₇₀ days

= 16 ⁴¹/₇₀ days or 16.586

Thus, Patricia and William together will finish the work in 16 ⁴¹/₇₀ days or 16.586 days Answer

Similar Questions

(1) If Timothy can finish the work in 53 days and Tyler can finish the same work in 58 days, then in how many days both can finish the work together?

(2) If Elizabeth can finish the work in 11 days and Daniel can finish the same work in 15 days, then in how many days both can finish the work together?

(3) If Carol can finish the work in 46 days and Alexander can finish the same work in 51 days, then in how many days both can finish the work together?

(4) Jennifer can finish a work in 6 days. Linda can finish the same work in 7 days while Elizabeth can finish the work in 8 days. How long will it take to finish it if they work together?

(5) 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?

(6) Nicholas can finish a work in 69 days. Jonathan can finish the same work in 74 days while Stephen can finish the work in 79 days. How long will it take to finish it if they work together?

(7) If Scott can finish the work in 81 days and Bryan can finish the same work in 86 days, then in how many days both can finish the work together?

(8) Laura can finish a work in 62 days. Kathleen can finish the same work in 67 days while Amy can finish the work in 72 days. How long will it take to finish it if they work together?

(9) If Mary can finish the work in 6 days and Michael can finish the same work in 11 days, then in how many days both can finish the work together?

(10) If Samantha can finish the work in 86 days and Logan can finish the same work in 91 days, then in how many days both can finish the work together?