Time and Work
Math MCQs

Question :    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?

Correct Answer  51 ⁹/₄₁ days or 51.22 days

Solution & Explanation

Solution

Given,

The number of days to finish the work by Catherine = 100 days

And, the number of days to finish the same work by Mason = 105 days

Thus, the number of days to finish the work by Catherine and Mason together = ?

Here,

∵ In 100 days the work done by Catherine = 1

∴ In 1 day, the work done by Catherine = ¹/₁₀₀ part

Similarly,

∵ In 105 days the work done by Mason = 1

∴ In 1 day, the work done by Mason = ¹/₁₀₅ part

Now, in 1 day, the work done by Catherine and Mason together

= In 1 day work done by Catherine + In 1 day the work done by Mason

= ¹/₁₀₀ + ¹/₁₀₅

= ^{21 + 20}/₂₁₀₀

= ⁴¹/₂₁₀₀ part of work

This means in 1 day, ⁴¹/₂₁₀₀ part of work is done by Catherine and Mason working together.

Now, the number of days required to finish ⁴¹/₂₁₀₀ part of work by Catherine + Mason working together = 1

∴ the number of days required to finish 1 work by Catherine + Mason together

= ¹/_⁴¹/2100

= 1 × ²¹⁰⁰/₄₁ = ²¹⁰⁰/₄₁ days

= 51 ⁹/₄₁ days = or 51.22 days

Thus, Catherine and Mason working together will finish the work in 51 ⁹/₄₁ days = or 51.22 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 Catherine = 100 days

And the number of days required to finish the same work by Mason = 105 days

Thus, the number of days required to finish the work Catherine and Mason working together = ?

Here a = 100 days

And, b = 105 days

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

The number of days required to finish the work when Catherine and Mason working together

= ^{100 × 105}/_{100 + 105} days

= ¹⁰⁵⁰⁰/₂₀₅ days

= ^{10500 ÷ 5}/_{205 ÷ 5} = ²¹⁰⁰/₄₁ days

= 51 ⁹/₄₁ days or 51.22

Thus, Catherine and Mason together will finish the work in 51 ⁹/₄₁ days or 51.22 days Answer

Similar Questions

(1) If James can finish the work in 24 days and John can finish the same work in 40 days, then in how many days both can finish the work together?

(2) If Jessica can finish the work in 17 days and Paul can finish the same work in 21 days, then in how many days both can finish the work together?

(3) If Emily can finish the work in 40 days and Justin can finish the same work in 45 days, then in how many days both can finish the work together?

(4) If John can finish the work in 6 days and Richard can finish the same work in 9 days, then in how many days both can finish the work together?

(5) 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?

(6) Samantha can finish a work in 86 days. Christine can finish the same work in 91 days while Debra can finish the work in 96 days. How long will it take to finish it if they work together?

(7) 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?

(8) If Samantha can finish the work in 86 days and Logan can finish the same work in 91 days, then in how many days both can finish the work together?

(9) If Michelle can finish the work in 41 days and Samuel can finish the same work in 44 days, then in how many days both can finish the work together?

(10) If Paul can finish the work in 36 days and Larry can finish the same work in 40 days, then in how many days both can finish the work together?