Time and Work
MCQs Math


Question:     If Angela can finish the work in 70 days and Terry can finish the same work in 75 days, then in how many days both can finish the work together?


Correct Answer  36 6/29 days or 36.207 days

Solution And Explanation

Solution

Given,

The number of days to finish the work by Angela = 70 days

And, the number of days to finish the same work by Terry = 75 days

Thus, the number of days to finish the work by Angela and Terry together = ?

Here,

∵ In 70 days the work done by Angela = 1

∴ In 1 day, the work done by Angela = 1/70 part

Similarly,

∵ In 75 days the work done by Terry = 1

∴ In 1 day, the work done by Terry = 1/75 part

Now, in 1 day, the work done by Angela and Terry together

= In 1 day work done by Angela + In 1 day the work done by Terry

= 1/70 + 1/75

= 15 + 14/1050

= 29/1050 part of work

This means in 1 day, 29/1050 part of work is done by Angela and Terry working together.

Now, the number of days required to finish 29/1050 part of work by Angela + Terry working together = 1

∴ the number of days required to finish 1 work by Angela + Terry together

= 1/29/1050

= 1 × 1050/29 = 1050/29 days

= 36 6/29 days = or 36.207 days

Thus, Angela and Terry working together will finish the work in 36 6/29 days = or 36.207 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 Angela = 70 days

And the number of days required to finish the same work by Terry = 75 days

Thus, the number of days required to finish the work Angela and Terry working together = ?

Here a = 70 days

And, b = 75 days

Thus, using formula a × b/a + b days

The number of days required to finish the work when Angela and Terry working together

= 70 × 75/70 + 75 days

= 5250/145 days

= 5250 ÷ 5/145 ÷ 5 = 1050/29 days

= 36 6/29 days or 36.207

Thus, Angela and Terry together will finish the work in 36 6/29 days or 36.207 days Answer


Similar Questions

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(2) If John can finish the work in 9 days and Richard can finish the same work in 14 days, then in how many days both can finish the work together?

(3) Melissa can finish a work in 52 days. Stephanie can finish the same work in 57 days while Rebecca can finish the work in 62 days. How long will it take to finish it if they work together?

(4) If Paul can finish the work in 36 days and Larry can finish the same work in 39 days, then in how many days both can finish the work together?

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(6) If Carolyn can finish the work in 96 days and Ralph can finish the same work in 101 days, then in how many days both can finish the work together?

(7) If Kenneth can finish the work in 45 days and Gregory can finish the same work in 50 days, then in how many days both can finish the work together?

(8) If Myra can finish the work in 25 days and Sophia can finish the same work in 15 days, then in how many days they both can finish the work working together?

(9) Anthony can finish a work in 27 days. Mark can finish the same work in 28 days while Donald can finish the work in 29 days. How long will it take to finish it if they work together?

(10) If Lisa can finish the work in 23 days and George can finish the same work in 26 days, then in how many days both can finish the work together?


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