Time and Work
Math MCQs

Question :    If Sharon can finish the work in 60 days and Zachary can finish the same work in 65 days, then in how many days both can finish the work together?

Correct Answer  31 ¹/₅ days or 31.2 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Sharon = 60 days

And, the number of days to finish the same work by Zachary = 65 days

Thus, the number of days to finish the work by Sharon and Zachary together = ?

Here,

∵ In 60 days the work done by Sharon = 1

∴ In 1 day, the work done by Sharon = ¹/₆₀ part

Similarly,

∵ In 65 days the work done by Zachary = 1

∴ In 1 day, the work done by Zachary = ¹/₆₅ part

Now, in 1 day, the work done by Sharon and Zachary together

= In 1 day work done by Sharon + In 1 day the work done by Zachary

= ¹/₆₀ + ¹/₆₅

= ^{13 + 12}/₇₈₀

= ²⁵/₇₈₀ part of work

= ^{25 ÷ 5}/_{780 ÷ 5} part of work

= ⁵/₁₅₆ part of work

This means, in 1 day, ⁵/₁₅₆ part of the work is done by Sharon and Zachary together.

Now, the number of days required to finish ⁵/₁₅₆ part of work by Sharon + Zachary working together = 1

∴ the number of days required to finish 1 work by Sharon + Zachary together

= ¹/_⁵/156

= 1 × ¹⁵⁶/₅ = ¹⁵⁶/₅ days

= 31 ¹/₅ days = or 31.2 days

Thus, Sharon and Zachary working together will finish the work in 31 ¹/₅ days = or 31.2 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 Sharon = 60 days

And the number of days required to finish the same work by Zachary = 65 days

Thus, the number of days required to finish the work Sharon and Zachary working together = ?

Here a = 60 days

And, b = 65 days

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

The number of days required to finish the work when Sharon and Zachary working together

= ^{60 × 65}/_{60 + 65} days

= ³⁹⁰⁰/₁₂₅ days

= ^{3900 ÷ 25}/_{125 ÷ 25} = ¹⁵⁶/₅ days

= 31 ¹/₅ days or 31.2

Thus, Sharon and Zachary together will finish the work in 31 ¹/₅ days or 31.2 days Answer

Similar Questions

(1) If Barbara can finish the work in 13 days and Anthony can finish the same work in 17 days, then in how many days both can finish the work together?

(2) If Benjamin can finish the work in 85 days and Gabriel can finish the same work in 90 days, then in how many days both can finish the work together?

(3) Patricia can finish a work in 4 days. Jennifer can finish the same work in 5 days while Linda can finish the work in 6 days. How long will it take to finish it if they work together?

(4) If Stephanie can finish the work in 56 days and Adam can finish the same work in 61 days, then in how many days both can finish the work together?

(5) 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?

(6) 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?

(7) If Lisa can finish the work in 26 days and George can finish the same work in 31 days, then in how many days both can finish the work together?

(8) If Joseph can finish the work in 19 days and Steven can finish the same work in 24 days, then in how many days both can finish the work together?

(9) Scott can finish a work in 81 days. Benjamin can finish the same work in 86 days while Samuel can finish the work in 91 days. How long will it take to finish it if they work together?

(10) Laura can finish a work in 62 days. Kathleen can finish the same work in 67 days while Amy can finish the work in 72 days. How long will it take to finish it if they work together?