Time and Work
Math MCQs

Question :    If Carol can finish the work in 43 days and Alexander can finish the same work in 47 days, then in how many days both can finish the work together?

Correct Answer  22 ⁴¹/₉₀ days or 22.456 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Carol = 43 days

And, the number of days to finish the same work by Alexander = 47 days

Thus, the number of days to finish the work by Carol and Alexander together = ?

Here,

∵ In 43 days the work done by Carol = 1

∴ In 1 day, the work done by Carol = ¹/₄₃ part

Similarly,

∵ In 47 days the work done by Alexander = 1

∴ In 1 day, the work done by Alexander = ¹/₄₇ part

Now, in 1 day, the work done by Carol and Alexander together

= In 1 day work done by Carol + In 1 day the work done by Alexander

= ¹/₄₃ + ¹/₄₇

= ^{47 + 43}/₂₀₂₁

= ⁹⁰/₂₀₂₁ part of work

This means in 1 day, ⁹⁰/₂₀₂₁ part of work is done by Carol and Alexander working together.

Now, the number of days required to finish ⁹⁰/₂₀₂₁ part of work by Carol + Alexander working together = 1

∴ the number of days required to finish 1 work by Carol + Alexander together

= ¹/_⁹⁰/2021

= 1 × ²⁰²¹/₉₀ = ²⁰²¹/₉₀ days

= 22 ⁴¹/₉₀ days = or 22.456 days

Thus, Carol and Alexander working together will finish the work in 22 ⁴¹/₉₀ days = or 22.456 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 Carol = 43 days

And the number of days required to finish the same work by Alexander = 47 days

Thus, the number of days required to finish the work Carol and Alexander working together = ?

Here a = 43 days

And, b = 47 days

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

The number of days required to finish the work when Carol and Alexander working together

= ^{43 × 47}/_{43 + 47} days

= ²⁰²¹/₉₀ days

= 22 ⁴¹/₉₀ days or 22.456

Thus, Carol and Alexander together will finish the work in 22 ⁴¹/₉₀ days or 22.456 days Answer

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