Time and Work
Math MCQs

Question :    If Christopher can finish the work in 22 days and Brian can finish the same work in 26 days, then in how many days both can finish the work together?

Correct Answer  11 ¹¹/₁₂ days or 11.917 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Christopher = 22 days

And, the number of days to finish the same work by Brian = 26 days

Thus, the number of days to finish the work by Christopher and Brian together = ?

Here,

∵ In 22 days the work done by Christopher = 1

∴ In 1 day, the work done by Christopher = ¹/₂₂ part

Similarly,

∵ In 26 days the work done by Brian = 1

∴ In 1 day, the work done by Brian = ¹/₂₆ part

Now, in 1 day, the work done by Christopher and Brian together

= In 1 day work done by Christopher + In 1 day the work done by Brian

= ¹/₂₂ + ¹/₂₆

= ^{13 + 11}/₂₈₆

= ²⁴/₂₈₆ part of work

= ^{24 ÷ 2}/_{286 ÷ 2} part of work

= ¹²/₁₄₃ part of work

This means, in 1 day, ¹²/₁₄₃ part of the work is done by Christopher and Brian together.

Now, the number of days required to finish ¹²/₁₄₃ part of work by Christopher + Brian working together = 1

∴ the number of days required to finish 1 work by Christopher + Brian together

= ¹/_¹²/143

= 1 × ¹⁴³/₁₂ = ¹⁴³/₁₂ days

= 11 ¹¹/₁₂ days = or 11.917 days

Thus, Christopher and Brian working together will finish the work in 11 ¹¹/₁₂ days = or 11.917 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 Christopher = 22 days

And the number of days required to finish the same work by Brian = 26 days

Thus, the number of days required to finish the work Christopher and Brian working together = ?

Here a = 22 days

And, b = 26 days

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

The number of days required to finish the work when Christopher and Brian working together

= ^{22 × 26}/_{22 + 26} days

= ⁵⁷²/₄₈ days

= ^{572 ÷ 4}/_{48 ÷ 4} = ¹⁴³/₁₂ days

= 11 ¹¹/₁₂ days or 11.917

Thus, Christopher and Brian together will finish the work in 11 ¹¹/₁₂ days or 11.917 days Answer

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