Time and Work
MCQs Math


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 And 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) Gregory can finish a work in 89 days. Frank can finish the same work in 94 days while Patrick can finish the work in 99 days. How long will it take to finish it if they work together?

(2) If Michelle can finish the work in 41 days and Samuel can finish the same work in 45 days, then in how many days both can finish the work together?

(3) If Gregory can finish the work in 89 days and Alan can finish the same work in 94 days, then in how many days both can finish the work together?

(4) If Emma can finish the work in 80 days and Jordan can finish the same work in 85 days, then in how many days both can finish the work together?

(5) If John can finish the work in 6 days and Richard can finish the same work in 10 days, then in how many days both can finish the work together?

(6) If Daniel can finish the work in 27 days and Timothy can finish the same work in 32 days, then in how many days both can finish the work together?

(7) Kevin can finish a work in 47 days. George can finish the same work in 52 days while Timothy can finish the work in 57 days. How long will it take to finish it if they work together?

(8) Catherine can finish a work in 100 days. Heather can finish the same work in 105 days while Diane can finish the work in 110 days. How long will it take to finish it if they work together?

(9) 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?

(10) Matthew can finish a work in 25 days. Anthony can finish the same work in 26 days while Mark can finish the work in 27 days. How long will it take to finish it if they work together?


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