Time and Work
Math MCQs

Question :    If Ronald can finish the work in 55 days and Jose can finish the same work in 60 days, then in how many days both can finish the work together?

Correct Answer  28 ¹⁶/₂₃ days or 28.696 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Ronald = 55 days

And, the number of days to finish the same work by Jose = 60 days

Thus, the number of days to finish the work by Ronald and Jose together = ?

Here,

∵ In 55 days the work done by Ronald = 1

∴ In 1 day, the work done by Ronald = ¹/₅₅ part

Similarly,

∵ In 60 days the work done by Jose = 1

∴ In 1 day, the work done by Jose = ¹/₆₀ part

Now, in 1 day, the work done by Ronald and Jose together

= In 1 day work done by Ronald + In 1 day the work done by Jose

= ¹/₅₅ + ¹/₆₀

= ^{12 + 11}/₆₆₀

= ²³/₆₆₀ part of work

This means in 1 day, ²³/₆₆₀ part of work is done by Ronald and Jose working together.

Now, the number of days required to finish ²³/₆₆₀ part of work by Ronald + Jose working together = 1

∴ the number of days required to finish 1 work by Ronald + Jose together

= ¹/_²³/660

= 1 × ⁶⁶⁰/₂₃ = ⁶⁶⁰/₂₃ days

= 28 ¹⁶/₂₃ days = or 28.696 days

Thus, Ronald and Jose working together will finish the work in 28 ¹⁶/₂₃ days = or 28.696 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 Ronald = 55 days

And the number of days required to finish the same work by Jose = 60 days

Thus, the number of days required to finish the work Ronald and Jose working together = ?

Here a = 55 days

And, b = 60 days

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

The number of days required to finish the work when Ronald and Jose working together

= ^{55 × 60}/_{55 + 60} days

= ³³⁰⁰/₁₁₅ days

= ^{3300 ÷ 5}/_{115 ÷ 5} = ⁶⁶⁰/₂₃ days

= 28 ¹⁶/₂₃ days or 28.696

Thus, Ronald and Jose together will finish the work in 28 ¹⁶/₂₃ days or 28.696 days Answer

Similar Questions

(1) If Kathleen can finish the work in 66 days and Jeremy can finish the same work in 71 days, then in how many days both can finish the work together?

(2) If Paul can finish the work in 39 days and Larry can finish the same work in 44 days, then in how many days both can finish the work together?

(3) Sharon can finish a work in 60 days. Cynthia can finish the same work in 65 days while Kathleen can finish the work in 70 days. How long will it take to finish it if they work together?

(4) If Sandra can finish the work in 34 days and Gary can finish the same work in 39 days, then in how many days both can finish the work together?

(5) John can finish a work in 9 days. David can finish the same work in 14 days while William can finish the work in 19 days. How long will it take to finish it if they work together?

(6) If John can finish the work in 9 days and Richard can finish the same work in 14 days, then in how many days both can finish the work together?

(7) If Thomas can finish the work in 18 days and Andrew can finish the same work in 22 days, then in how many days both can finish the work together?

(8) If A can do a piece of work in 2 days, B can do the same piece of work in 3 days, while C alone can do the same work in 4 days. Find the number of days to finish the work when they all will work together.

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(10) Jessica can finish a work in 20 days. Karen can finish the same work in 25 days while Lisa can finish the work in 30 days. How long will it take to finish it if they work together?