Time and Work
Math MCQs

Question :    If Betty can finish the work in 27 days and Jason can finish the same work in 30 days, then in how many days both can finish the work together?

Correct Answer  14 ⁴/₁₉ days or 14.211 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Betty = 27 days

And, the number of days to finish the same work by Jason = 30 days

Thus, the number of days to finish the work by Betty and Jason together = ?

Here,

∵ In 27 days the work done by Betty = 1

∴ In 1 day, the work done by Betty = ¹/₂₇ part

Similarly,

∵ In 30 days the work done by Jason = 1

∴ In 1 day, the work done by Jason = ¹/₃₀ part

Now, in 1 day, the work done by Betty and Jason together

= In 1 day work done by Betty + In 1 day the work done by Jason

= ¹/₂₇ + ¹/₃₀

= ^{10 + 9}/₂₇₀

= ¹⁹/₂₇₀ part of work

This means in 1 day, ¹⁹/₂₇₀ part of work is done by Betty and Jason working together.

Now, the number of days required to finish ¹⁹/₂₇₀ part of work by Betty + Jason working together = 1

∴ the number of days required to finish 1 work by Betty + Jason together

= ¹/_¹⁹/270

= 1 × ²⁷⁰/₁₉ = ²⁷⁰/₁₉ days

= 14 ⁴/₁₉ days = or 14.211 days

Thus, Betty and Jason working together will finish the work in 14 ⁴/₁₉ days = or 14.211 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 Betty = 27 days

And the number of days required to finish the same work by Jason = 30 days

Thus, the number of days required to finish the work Betty and Jason working together = ?

Here a = 27 days

And, b = 30 days

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

The number of days required to finish the work when Betty and Jason working together

= ^{27 × 30}/_{27 + 30} days

= ⁸¹⁰/₅₇ days

= ^{810 ÷ 3}/_{57 ÷ 3} = ²⁷⁰/₁₉ days

= 14 ⁴/₁₉ days or 14.211

Thus, Betty and Jason together will finish the work in 14 ⁴/₁₉ days or 14.211 days Answer

Similar Questions

(1) If Charles can finish the work in 20 days and Kenneth can finish the same work in 23 days, then in how many days both can finish the work together?

(2) If Catherine can finish the work in 100 days and Mason can finish the same work in 105 days, then in how many days both can finish the work together?

(3) If Dorothy can finish the work in 50 days and Jack can finish the same work in 55 days, then in how many days both can finish the work together?

(4) If Shirley can finish the work in 72 days and Harold can finish the same work in 77 days, then in how many days both can finish the work together?

(5) If Richard can finish the work in 17 days and Mark can finish the same work in 22 days, then in how many days both can finish the work together?

(6) If Robert can finish a work in 4 days and Bob can finish the same work in 6 days, then in how many days they both can finish the work working together?

(7) Stephanie can finish a work in 56 days. Sharon can finish the same work in 61 days while Laura can finish the work in 66 days. How long will it take to finish it if they work together?

(8) If William can finish the work in 34 days and Matthew can finish the same work in 50 days, then in how many days both can finish the work together?

(9) Nancy can finish a work in 24 days. Betty can finish the same work in 25 days while Margaret can finish the work in 26 days. How long will it take to finish it if they work together?

(10) Sandra can finish a work in 34 days. Kimberly can finish the same work in 39 days while Emily can finish the work in 44 days. How long will it take to finish it if they work together?