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

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