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Word Problems Quiz - CBSE Class 8 Mathematics

Free practice quiz: Word Problems (CBSE Class 8 Mathematics). 13 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 8 Mathematics practice quiz has 13 multiple-choice questions on Word Problems, and 13 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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Turning Words into Equations

  • Choose a letter, like x, for the unknown quantity and write what it stands for.
  • Increased by or more than means add; decreased by or less than means subtract.
  • Times means multiply, and the words is, equals or results in mean the equals sign.
a more than x
\[x + a\]
a less than x
\[x - a\]
k times x, decreased by a
\[kx - a\]
Two numbers with difference d
\[a \text{ and } a + d\]

Common mistake: Writing 'a less than x' as a - x. The correct expression is x - a, because a is taken away from x.

Solving by Transposing Terms

  • Move a term to the other side of the equation and change its sign.
  • A multiplier on one side becomes a divisor on the other side.
  • Do the same operation on both sides to keep the equation balanced.
Remove an added term
\[x + a = b \Rightarrow x = b - a\]
Remove a subtracted term
\[x - a = b \Rightarrow x = b + a\]
Remove a multiplier
\[kx = b \Rightarrow x = \frac{b}{k}, \; k \neq 0\]

Common mistake: Moving a term across the equals sign without changing its sign, for example turning +a into +a instead of -a.

Consecutive Numbers

  • Consecutive numbers follow one after another with the same gap d between them.
  • For consecutive integers d is 1. For consecutive even or odd numbers, d is double that.
Three consecutive numbers with gap d
\[x,\; x + d,\; x + d + d\]
Consecutive integers
\[n,\; n + 1\]

Common mistake: Using a gap of 1 for consecutive even numbers. Even numbers skip one integer between them, so the gap is double that.

Everyday Formulas in Word Problems

  • Speed, distance and time are linked. If you know two of them, you can find the third.
  • Total money equals price per item multiplied by the number of items.
  • The area of a rectangle equals its length multiplied by its width.
Distance
\[\text{Distance} = \text{Speed} \times \text{Time}\]
Speed
\[\text{Speed} = \frac{\text{Distance}}{\text{Time}}\]
Revenue
\[R = p \times x\]
Area of rectangle
\[A = l \times w\]

Common mistake: Dividing time by distance to get speed. Speed is distance divided by time.

Exam tips

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

  1. A number is increased by 5 and the result is 12. What is the number?

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    Answer: A. 7

    Let the number be x. According to the problem, x + 5 = 12. Solving this gives x = 12 - 5 = 7.

  2. A train travels a distance of 180 km at a uniform speed. If it takes 3 hours to cover the distance, what is the speed of the train?

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    Answer: B. 60 km/h

    Speed is calculated as distance divided by time. So, speed = 180 km / 3 hours = 60 km/h.

  3. The sum of two consecutive integers is 47. What are the integers?

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    Answer: A. 23 and 24

    Let the first integer be n. The next consecutive integer is n + 1. Hence, n + (n + 1) = 47. This simplifies to 2n + 1 = 47, giving n = 23.

  4. A car travels at a speed of 80 km/h and takes x hours to travel 320 kilometers. What is the value of x?

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    Answer: C. 4

    Using the formula speed = distance / time, we have 80 = 320 / x, which gives x = 320 / 80 = 4.

  5. Twice a number decreased by 8 equals 10. What is the number?

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    Answer: A. 9

    Let the number be n. The equation is 2n - 8 = 10. Solving gives 2n = 18, so n = 9.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. If 3 times a number is decreased by 4, the result is 5. What is the number?
  2. A man has $50 more than twice the amount of money his friend has. If his friend has x dollars, how much money does the man have?
  3. If 5 years are added to a person's age, the result will be 20 years. What is the current age of the person?
  4. Two numbers have a difference of 12. If one number is represented as a, what is the equation representing the other number?
  5. If the price of a notebook decreases by $2 and the new price is $5, what was the original price?
  6. What is the equation for the total revenue from selling x items at a price of p dollars each?
  7. A room's dimensions are length 4 meters longer than the width. If the width is x meters, and the area is 84 square meters, what is the width?
  8. The sum of three consecutive even numbers is 48. What are the numbers?

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