Time and Work
Math MCQs

Question :    If Carol can finish the work in 43 days and Alexander can finish the same work in 46 days, then in how many days both can finish the work together?

Correct Answer  22 ²⁰/₈₉ days or 22.225 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 = 46 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 46 days the work done by Alexander = 1

∴ In 1 day, the work done by Alexander = ¹/₄₆ 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 + ¹/₄₆

= ^{46 + 43}/₁₉₇₈

= ⁸⁹/₁₉₇₈ part of work

This means in 1 day, ⁸⁹/₁₉₇₈ part of work is done by Carol and Alexander working together.

Now, the number of days required to finish ⁸⁹/₁₉₇₈ part of work by Carol + Alexander working together = 1

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

= ¹/_⁸⁹/1978

= 1 × ¹⁹⁷⁸/₈₉ = ¹⁹⁷⁸/₈₉ days

= 22 ²⁰/₈₉ days = or 22.225 days

Thus, Carol and Alexander working together will finish the work in 22 ²⁰/₈₉ days = or 22.225 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 = 46 days

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

Here a = 43 days

And, b = 46 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 × 46}/_{43 + 46} days

= ¹⁹⁷⁸/₈₉ days

= 22 ²⁰/₈₉ days or 22.225

Thus, Carol and Alexander together will finish the work in 22 ²⁰/₈₉ days or 22.225 days Answer

Similar Questions

(1) 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?

(2) If Carol can finish the work in 43 days and Alexander can finish the same work in 46 days, then in how many days both can finish the work together?

(3) If Mary can finish the work in 3 days and Michael can finish the same work in 7 days, then in how many days both can finish the work together?

(4) 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?

(5) If Jack can finish the work in 20 days and Bill can finish the same work in 30 days, then in how many days they both can finish the work working together?

(6) Andrew can finish a work in 37 days. Joshua can finish the same work in 38 days while Kenneth can finish the work in 39 days. How long will it take to finish it if they work together?

(7) If Ashley can finish the work in 36 days and Eric can finish the same work in 41 days, then in how many days both can finish the work together?

(8) If Laura can finish the work in 62 days and Kyle can finish the same work in 67 days, then in how many days both can finish the work together?

(9) If Sandra can finish the work in 31 days and Gary can finish the same work in 34 days, then in how many days both can finish the work together?

(10) If Michael can finish the work in 11 days and Thomas can finish the same work in 16 days, then in how many days both can finish the work together?