Time and Work
Math MCQs

Question :    If Nancy can finish the work in 28 days and Ronald can finish the same work in 33 days, then in how many days both can finish the work together?

Correct Answer  15 ⁹/₆₁ days or 15.148 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Nancy = 28 days

And, the number of days to finish the same work by Ronald = 33 days

Thus, the number of days to finish the work by Nancy and Ronald together = ?

Here,

∵ In 28 days the work done by Nancy = 1

∴ In 1 day, the work done by Nancy = ¹/₂₈ part

Similarly,

∵ In 33 days the work done by Ronald = 1

∴ In 1 day, the work done by Ronald = ¹/₃₃ part

Now, in 1 day, the work done by Nancy and Ronald together

= In 1 day work done by Nancy + In 1 day the work done by Ronald

= ¹/₂₈ + ¹/₃₃

= ^{33 + 28}/₉₂₄

= ⁶¹/₉₂₄ part of work

This means in 1 day, ⁶¹/₉₂₄ part of work is done by Nancy and Ronald working together.

Now, the number of days required to finish ⁶¹/₉₂₄ part of work by Nancy + Ronald working together = 1

∴ the number of days required to finish 1 work by Nancy + Ronald together

= ¹/_⁶¹/924

= 1 × ⁹²⁴/₆₁ = ⁹²⁴/₆₁ days

= 15 ⁹/₆₁ days = or 15.148 days

Thus, Nancy and Ronald working together will finish the work in 15 ⁹/₆₁ days = or 15.148 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 Nancy = 28 days

And the number of days required to finish the same work by Ronald = 33 days

Thus, the number of days required to finish the work Nancy and Ronald working together = ?

Here a = 28 days

And, b = 33 days

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

The number of days required to finish the work when Nancy and Ronald working together

= ^{28 × 33}/_{28 + 33} days

= ⁹²⁴/₆₁ days

= 15 ⁹/₆₁ days or 15.148

Thus, Nancy and Ronald together will finish the work in 15 ⁹/₆₁ days or 15.148 days Answer

Similar Questions

(1) If Dorothy can finish the work in 47 days and Jack can finish the same work in 51 days, then in how many days both can finish the work together?

(2) 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?

(3) Eric can finish a work in 71 days. Stephen can finish the same work in 76 days while Larry can finish the work in 81 days. How long will it take to finish it if they work together?

(4) Debra can finish a work in 92 days. Carolyn can finish the same work in 97 days while Janet can finish the work in 102 days. How long will it take to finish it if they work together?

(5) If Jennifer can finish the work in 7 days and Joseph can finish the same work in 10 days, then in how many days both can finish the work together?

(6) Christine can finish a work in 90 days. Rachel can finish the same work in 95 days while Carolyn can finish the work in 100 days. How long will it take to finish it if they work together?

(7) If Brandon can finish the work in 83 days and Joe can finish the same work in 88 days, then in how many days both can finish the work together?

(8) Kathleen can finish a work in 66 days. Angela can finish the same work in 71 days while Shirley can finish the work in 76 days. How long will it take to finish it if they work together?

(9) Anthony can finish a work in 31 days. Donald can finish the same work in 36 days while Steven can finish the work in 41 days. How long will it take to finish it if they work together?

(10) Ronald can finish a work in 55 days. Jason can finish the same work in 60 days while Jeffrey can finish the work in 65 days. How long will it take to finish it if they work together?