Time and Work
Math MCQs

Question :    If Christine can finish the work in 90 days and Juan can finish the same work in 95 days, then in how many days both can finish the work together?

Correct Answer  46 ⁸/₃₇ days or 46.216 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Christine = 90 days

And, the number of days to finish the same work by Juan = 95 days

Thus, the number of days to finish the work by Christine and Juan together = ?

Here,

∵ In 90 days the work done by Christine = 1

∴ In 1 day, the work done by Christine = ¹/₉₀ part

Similarly,

∵ In 95 days the work done by Juan = 1

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

Now, in 1 day, the work done by Christine and Juan together

= In 1 day work done by Christine + In 1 day the work done by Juan

= ¹/₉₀ + ¹/₉₅

= ^{19 + 18}/₁₇₁₀

= ³⁷/₁₇₁₀ part of work

This means in 1 day, ³⁷/₁₇₁₀ part of work is done by Christine and Juan working together.

Now, the number of days required to finish ³⁷/₁₇₁₀ part of work by Christine + Juan working together = 1

∴ the number of days required to finish 1 work by Christine + Juan together

= ¹/_³⁷/1710

= 1 × ¹⁷¹⁰/₃₇ = ¹⁷¹⁰/₃₇ days

= 46 ⁸/₃₇ days = or 46.216 days

Thus, Christine and Juan working together will finish the work in 46 ⁸/₃₇ days = or 46.216 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 Christine = 90 days

And the number of days required to finish the same work by Juan = 95 days

Thus, the number of days required to finish the work Christine and Juan working together = ?

Here a = 90 days

And, b = 95 days

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

The number of days required to finish the work when Christine and Juan working together

= ^{90 × 95}/_{90 + 95} days

= ⁸⁵⁵⁰/₁₈₅ days

= ^{8550 ÷ 5}/_{185 ÷ 5} = ¹⁷¹⁰/₃₇ days

= 46 ⁸/₃₇ days or 46.216

Thus, Christine and Juan together will finish the work in 46 ⁸/₃₇ days or 46.216 days Answer

Similar Questions

(1) Nancy can finish a work in 24 days. Betty can finish the same work in 25 days while Margaret can finish the work in 26 days. How long will it take to finish it if they work together?

(2) 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?

(3) If Anthony can finish the work in 28 days and Jeffrey can finish the same work in 31 days, then in how many days both can finish the work together?

(4) If Karen can finish the work in 21 days and Kevin can finish the same work in 25 days, then in how many days both can finish the work together?

(5) Sandra can finish a work in 34 days. Kimberly can finish the same work in 39 days while Emily can finish the work in 44 days. How long will it take to finish it if they work together?

(6) Nicole can finish a work in 82 days. Samantha can finish the same work in 87 days while Katherine can finish the work in 92 days. How long will it take to finish it if they work together?

(7) 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?

(8) Shirley can finish a work in 72 days. Brenda can finish the same work in 77 days while Pamela can finish the work in 82 days. How long will it take to finish it if they work together?

(9) If Anthony can finish the work in 28 days and Jeffrey can finish the same work in 32 days, then in how many days both can finish the work together?

(10) Karen can finish a work in 20 days. Lisa can finish the same work in 21 days while Nancy can finish the work in 22 days. How long will it take to finish it if they work together?