Time and Work
Math MCQs

Question :    If Christopher can finish the work in 25 days and Brian can finish the same work in 30 days, then in how many days both can finish the work together?

Correct Answer  13 ⁷/₁₁ days or 13.636 days

Solution & Explanation

Solution

Given,

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

And, the number of days to finish the same work by Brian = 30 days

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

Here,

∵ In 25 days the work done by Christopher = 1

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

Similarly,

∵ In 30 days the work done by Brian = 1

∴ In 1 day, the work done by Brian = ¹/₃₀ 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

= ¹/₂₅ + ¹/₃₀

= ^{6 + 5}/₁₅₀

= ¹¹/₁₅₀ part of work

This means in 1 day, ¹¹/₁₅₀ part of work is done by Christopher and Brian working together.

Now, the number of days required to finish ¹¹/₁₅₀ part of work by Christopher + Brian working together = 1

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

= ¹/_¹¹/150

= 1 × ¹⁵⁰/₁₁ = ¹⁵⁰/₁₁ days

= 13 ⁷/₁₁ days = or 13.636 days

Thus, Christopher and Brian working together will finish the work in 13 ⁷/₁₁ days = or 13.636 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 = 25 days

And the number of days required to finish the same work by Brian = 30 days

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

Here a = 25 days

And, b = 30 days

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

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

= ^{25 × 30}/_{25 + 30} days

= ⁷⁵⁰/₅₅ days

= ^{750 ÷ 5}/_{55 ÷ 5} = ¹⁵⁰/₁₁ days

= 13 ⁷/₁₁ days or 13.636

Thus, Christopher and Brian together will finish the work in 13 ⁷/₁₁ days or 13.636 days Answer

Similar Questions

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(2) If Brandon can finish the work in 83 days and Joe can finish the same work in 88 days, then in how many days both can finish the work together?

(3) If Amanda can finish the work in 45 days and Patrick can finish the same work in 48 days, then in how many days both can finish the work together?

(4) Kimberly can finish a work in 34 days. Emily can finish the same work in 35 days while Donna can finish the work in 36 days. How long will it take to finish it if they work together?

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(6) If William can finish the work in 34 days and Matthew can finish the same work in 50 days, then in how many days both can finish the work together?

(7) Margaret can finish a work in 28 days. Sandra can finish the same work in 29 days while Ashley can finish the work in 30 days. How long will it take to finish it if they work together?

(8) Elizabeth can finish a work in 10 days. Barbara can finish the same work in 11 days while Susan can finish the work in 12 days. How long will it take to finish it if they work together?

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(10) Rachel can finish a work in 94 days. Janet can finish the same work in 99 days while Catherine can finish the work in 104 days. How long will it take to finish it if they work together?