Time and Work
Math MCQs

Question :    If Andrew can finish the work in 38 days and Scott can finish the same work in 41 days, then in how many days both can finish the work together?

Correct Answer  19 ⁵⁷/₇₉ days or 19.722 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Andrew = 38 days

And, the number of days to finish the same work by Scott = 41 days

Thus, the number of days to finish the work by Andrew and Scott together = ?

Here,

∵ In 38 days the work done by Andrew = 1

∴ In 1 day, the work done by Andrew = ¹/₃₈ part

Similarly,

∵ In 41 days the work done by Scott = 1

∴ In 1 day, the work done by Scott = ¹/₄₁ part

Now, in 1 day, the work done by Andrew and Scott together

= In 1 day work done by Andrew + In 1 day the work done by Scott

= ¹/₃₈ + ¹/₄₁

= ^{41 + 38}/₁₅₅₈

= ⁷⁹/₁₅₅₈ part of work

This means in 1 day, ⁷⁹/₁₅₅₈ part of work is done by Andrew and Scott working together.

Now, the number of days required to finish ⁷⁹/₁₅₅₈ part of work by Andrew + Scott working together = 1

∴ the number of days required to finish 1 work by Andrew + Scott together

= ¹/_⁷⁹/1558

= 1 × ¹⁵⁵⁸/₇₉ = ¹⁵⁵⁸/₇₉ days

= 19 ⁵⁷/₇₉ days = or 19.722 days

Thus, Andrew and Scott working together will finish the work in 19 ⁵⁷/₇₉ days = or 19.722 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 Andrew = 38 days

And the number of days required to finish the same work by Scott = 41 days

Thus, the number of days required to finish the work Andrew and Scott working together = ?

Here a = 38 days

And, b = 41 days

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

The number of days required to finish the work when Andrew and Scott working together

= ^{38 × 41}/_{38 + 41} days

= ¹⁵⁵⁸/₇₉ days

= 19 ⁵⁷/₇₉ days or 19.722

Thus, Andrew and Scott together will finish the work in 19 ⁵⁷/₇₉ days or 19.722 days Answer

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