Topic Details (Notes format)

How to Solve Work-Rate Problems

Subject: Mathematics

Book: Maths Mastery

Work-rate problems revolve around the formula Work = Rate × Time, often focusing on collaborative tasks. For example, if Person A can complete a job in 6 hours (rate = 1/6 job/hour) and Person B can do it in 3 hours (rate = 1/3 job/hour), together their combined rate is 1/6 + 1/3 = 1/2 job/hour, so they finish in 2 hours. Work-rate logic extends to real-life scheduling—like painting rooms, manufacturing tasks, or data processing. Mastering these setups helps you optimize resource use, plan effectively, and interpret team-based productivity measurements.

Practice Questions

A number is increased by 20% and then decreased by 20%. What is the net change?

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The probability of getting an even number when rolling a die is:

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The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

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If the radius of a circle is doubled, what happens to its area?

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What is the square root of 121?

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If a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?

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If x - y = 5 and x + y = 15, what is the value of x?

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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How many diagonals does a pentagon have?

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If 3x = 81, what is the value of x?

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