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

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(2) If George can finish the work in 48 days and Dennis can finish the same work in 52 days, then in how many days both can finish the work together?

(3) If Linda can finish the work in 12 days and Charles can finish the same work in 17 days, then in how many days both can finish the work together?

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(7) If Jack can finish the work in 20 days and Bill can finish the same work in 30 days, then in how many days they both can finish the work working together?

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