Time and Work
MCQs Math


Question:     If Linda can finish the work in 9 days and Charles can finish the same work in 12 days, then in how many days both can finish the work together?


Correct Answer  5 1/7 days or 5.143 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Linda = 9 days

And, the number of days to finish the same work by Charles = 12 days

Thus, the number of days to finish the work by Linda and Charles together = ?

Here,

∵ In 9 days the work done by Linda = 1

∴ In 1 day, the work done by Linda = 1/9 part

Similarly,

∵ In 12 days the work done by Charles = 1

∴ In 1 day, the work done by Charles = 1/12 part

Now, in 1 day, the work done by Linda and Charles together

= In 1 day work done by Linda + In 1 day the work done by Charles

= 1/9 + 1/12

= 4 + 3/36

= 7/36 part of work

This means in 1 day, 7/36 part of work is done by Linda and Charles working together.

Now, the number of days required to finish 7/36 part of work by Linda + Charles working together = 1

∴ the number of days required to finish 1 work by Linda + Charles together

= 1/7/36

= 1 × 36/7 = 36/7 days

= 5 1/7 days = or 5.143 days

Thus, Linda and Charles working together will finish the work in 5 1/7 days = or 5.143 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 Linda = 9 days

And the number of days required to finish the same work by Charles = 12 days

Thus, the number of days required to finish the work Linda and Charles working together = ?

Here a = 9 days

And, b = 12 days

Thus, using formula a × b/a + b days

The number of days required to finish the work when Linda and Charles working together

= 9 × 12/9 + 12 days

= 108/21 days

= 108 ÷ 3/21 ÷ 3 = 36/7 days

= 5 1/7 days or 5.143

Thus, Linda and Charles together will finish the work in 5 1/7 days or 5.143 days Answer


Similar Questions

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