Time and Work
Math MCQs

Question :    If Nancy can finish the work in 25 days and Ronald can finish the same work in 28 days, then in how many days both can finish the work together?

Correct Answer  13 ¹¹/₅₃ days or 13.208 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Nancy = 25 days

And, the number of days to finish the same work by Ronald = 28 days

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

Here,

∵ In 25 days the work done by Nancy = 1

∴ In 1 day, the work done by Nancy = ¹/₂₅ part

Similarly,

∵ In 28 days the work done by Ronald = 1

∴ In 1 day, the work done by Ronald = ¹/₂₈ part

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

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

= ¹/₂₅ + ¹/₂₈

= ^{28 + 25}/₇₀₀

= ⁵³/₇₀₀ part of work

This means in 1 day, ⁵³/₇₀₀ part of work is done by Nancy and Ronald working together.

Now, the number of days required to finish ⁵³/₇₀₀ part of work by Nancy + Ronald working together = 1

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

= ¹/_⁵³/700

= 1 × ⁷⁰⁰/₅₃ = ⁷⁰⁰/₅₃ days

= 13 ¹¹/₅₃ days = or 13.208 days

Thus, Nancy and Ronald working together will finish the work in 13 ¹¹/₅₃ days = or 13.208 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 Nancy = 25 days

And the number of days required to finish the same work by Ronald = 28 days

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

Here a = 25 days

And, b = 28 days

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

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

= ^{25 × 28}/_{25 + 28} days

= ⁷⁰⁰/₅₃ days

= 13 ¹¹/₅₃ days or 13.208

Thus, Nancy and Ronald together will finish the work in 13 ¹¹/₅₃ days or 13.208 days Answer

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