Time and Work
Math MCQs

Question :    If Donald can finish the work in 32 days and Nicholas can finish the same work in 35 days, then in how many days both can finish the work together?

Correct Answer  16 ⁴⁸/₆₇ days or 16.716 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Donald = 32 days

And, the number of days to finish the same work by Nicholas = 35 days

Thus, the number of days to finish the work by Donald and Nicholas together = ?

Here,

∵ In 32 days the work done by Donald = 1

∴ In 1 day, the work done by Donald = ¹/₃₂ part

Similarly,

∵ In 35 days the work done by Nicholas = 1

∴ In 1 day, the work done by Nicholas = ¹/₃₅ part

Now, in 1 day, the work done by Donald and Nicholas together

= In 1 day work done by Donald + In 1 day the work done by Nicholas

= ¹/₃₂ + ¹/₃₅

= ^{35 + 32}/₁₁₂₀

= ⁶⁷/₁₁₂₀ part of work

This means in 1 day, ⁶⁷/₁₁₂₀ part of work is done by Donald and Nicholas working together.

Now, the number of days required to finish ⁶⁷/₁₁₂₀ part of work by Donald + Nicholas working together = 1

∴ the number of days required to finish 1 work by Donald + Nicholas together

= ¹/_⁶⁷/1120

= 1 × ¹¹²⁰/₆₇ = ¹¹²⁰/₆₇ days

= 16 ⁴⁸/₆₇ days = or 16.716 days

Thus, Donald and Nicholas working together will finish the work in 16 ⁴⁸/₆₇ days = or 16.716 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 Donald = 32 days

And the number of days required to finish the same work by Nicholas = 35 days

Thus, the number of days required to finish the work Donald and Nicholas working together = ?

Here a = 32 days

And, b = 35 days

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

The number of days required to finish the work when Donald and Nicholas working together

= ^{32 × 35}/_{32 + 35} days

= ¹¹²⁰/₆₇ days

= 16 ⁴⁸/₆₇ days or 16.716

Thus, Donald and Nicholas together will finish the work in 16 ⁴⁸/₆₇ days or 16.716 days Answer

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