Time and Work
Math MCQs

Question :    If George can finish the work in 48 days and Dennis can finish the same work in 52 days, then in how many days both can finish the work together?

Correct Answer  24 ²⁴/₂₅ days or 24.96 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by George = 48 days

And, the number of days to finish the same work by Dennis = 52 days

Thus, the number of days to finish the work by George and Dennis together = ?

Here,

∵ In 48 days the work done by George = 1

∴ In 1 day, the work done by George = ¹/₄₈ part

Similarly,

∵ In 52 days the work done by Dennis = 1

∴ In 1 day, the work done by Dennis = ¹/₅₂ part

Now, in 1 day, the work done by George and Dennis together

= In 1 day work done by George + In 1 day the work done by Dennis

= ¹/₄₈ + ¹/₅₂

= ^{13 + 12}/₆₂₄

= ²⁵/₆₂₄ part of work

This means in 1 day, ²⁵/₆₂₄ part of work is done by George and Dennis working together.

Now, the number of days required to finish ²⁵/₆₂₄ part of work by George + Dennis working together = 1

∴ the number of days required to finish 1 work by George + Dennis together

= ¹/_²⁵/624

= 1 × ⁶²⁴/₂₅ = ⁶²⁴/₂₅ days

= 24 ²⁴/₂₅ days = or 24.96 days

Thus, George and Dennis working together will finish the work in 24 ²⁴/₂₅ days = or 24.96 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 George = 48 days

And the number of days required to finish the same work by Dennis = 52 days

Thus, the number of days required to finish the work George and Dennis working together = ?

Here a = 48 days

And, b = 52 days

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

The number of days required to finish the work when George and Dennis working together

= ^{48 × 52}/_{48 + 52} days

= ²⁴⁹⁶/₁₀₀ days

= ^{2496 ÷ 4}/_{100 ÷ 4} = ⁶²⁴/₂₅ days

= 24 ²⁴/₂₅ days or 24.96

Thus, George and Dennis together will finish the work in 24 ²⁴/₂₅ days or 24.96 days Answer

Similar Questions

(1) If Kenneth can finish the work in 42 days and Gregory can finish the same work in 45 days, then in how many days both can finish the work together?

(2) If Mark can finish the work in 30 days and Jacob can finish the same work in 34 days, then in how many days both can finish the work together?

(3) If Donna can finish the work in 39 days and Brandon can finish the same work in 43 days, then in how many days both can finish the work together?

(4) 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?

(5) David can finish a work in 9 days. William can finish the same work in 10 days while Richard can finish the work in 11 days. How long will it take to finish it if they work together?

(6) If Timothy can finish the work in 53 days and Tyler can finish the same work in 58 days, then in how many days both can finish the work together?

(7) Mark can finish a work in 29 days. Donald can finish the same work in 30 days while Steven can finish the work in 31 days. How long will it take to finish it if they work together?

(8) If Robert can finish the work in 26 days and David can finish the same work in 42 days, then in how many days both can finish the work together?

(9) Steven can finish a work in 33 days. Paul can finish the same work in 34 days while Andrew can finish the work in 35 days. How long will it take to finish it if they work together?

(10) If Brian can finish the work in 46 days and Raymond can finish the same work in 50 days, then in how many days both can finish the work together?