Time and Work
Math MCQs

Question :    If Ryan can finish the work in 63 days and Ethan can finish the same work in 68 days, then in how many days both can finish the work together?

Correct Answer  32 ⁹²/₁₃₁ days or 32.702 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Ryan = 63 days

And, the number of days to finish the same work by Ethan = 68 days

Thus, the number of days to finish the work by Ryan and Ethan together = ?

Here,

∵ In 63 days the work done by Ryan = 1

∴ In 1 day, the work done by Ryan = ¹/₆₃ part

Similarly,

∵ In 68 days the work done by Ethan = 1

∴ In 1 day, the work done by Ethan = ¹/₆₈ part

Now, in 1 day, the work done by Ryan and Ethan together

= In 1 day work done by Ryan + In 1 day the work done by Ethan

= ¹/₆₃ + ¹/₆₈

= ^{68 + 63}/₄₂₈₄

= ¹³¹/₄₂₈₄ part of work

This means in 1 day, ¹³¹/₄₂₈₄ part of work is done by Ryan and Ethan working together.

Now, the number of days required to finish ¹³¹/₄₂₈₄ part of work by Ryan + Ethan working together = 1

∴ the number of days required to finish 1 work by Ryan + Ethan together

= ¹/_¹³¹/4284

= 1 × ⁴²⁸⁴/₁₃₁ = ⁴²⁸⁴/₁₃₁ days

= 32 ⁹²/₁₃₁ days = or 32.702 days

Thus, Ryan and Ethan working together will finish the work in 32 ⁹²/₁₃₁ days = or 32.702 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 Ryan = 63 days

And the number of days required to finish the same work by Ethan = 68 days

Thus, the number of days required to finish the work Ryan and Ethan working together = ?

Here a = 63 days

And, b = 68 days

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

The number of days required to finish the work when Ryan and Ethan working together

= ^{63 × 68}/_{63 + 68} days

= ⁴²⁸⁴/₁₃₁ days

= 32 ⁹²/₁₃₁ days or 32.702

Thus, Ryan and Ethan together will finish the work in 32 ⁹²/₁₃₁ days or 32.702 days Answer

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