Applications and Word Problems Quiz - CBSE Class 8 Mathematics
Free practice quiz: Applications and Word Problems (CBSE Class 8 Mathematics). 11 multiple-choice questions with answers and explanations. Play online, no sign-up needed.
This CBSE Class 8 Mathematics practice quiz has 11 multiple-choice questions on Applications and Word Problems, and 11 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
- Read the problem slowly and let one letter, like x, stand for the unknown quantity.
- Change each phrase into maths: 'more than' means add, 'less than' means subtract, 'times' means multiply.
- Words like 'is', 'gives' or 'the result is' become the equals sign in your equation.
Common mistake: Writing 'k less than x' as k − x. The correct expression is x − k, because k is taken away from x.
Express All Unknowns Using One Variable
- When two or more quantities are linked, write each one in terms of the same variable x.
- Consecutive integers go up by one each time. Consecutive even or odd numbers go up by two.
- For ages, every person's age increases by the same number of years, t, after t years.
Common mistake: Adding t years to only one person's age. Every person in the problem becomes t years older.
Geometry Facts for Word Problems
- Perimeter is the total length around a shape. For a rectangle, add all four sides.
- Supplementary angles add up to 180°. Complementary angles add up to 90°.
- Write one side or angle as x, and the other in terms of x.
Common mistake: Using l + b as the perimeter. That is only half of it, because a rectangle has two lengths and two widths.
Speed, Fractions and Money Rules
- Distance equals speed times time. A boat moving against the current goes slower, and with the current it goes faster.
- For fraction problems, let the denominator be x and write the numerator in terms of x.
- Profit is selling price minus cost price. Find the price of one item first.
Common mistake: For 'p items for Rs q', writing the price of one item as p/q. The correct price of one item is q/p rupees.
Exam tips
- Always write 'Let x = ...' clearly so you know exactly what your answer means.
- Check your answer by putting it back into the original word statement, not just into your equation.
- Answer the exact question asked, and include units like cm, km/h, years or rupees.
Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.
Sample questions
The sum of three consecutive integers is 36. What are the integers?
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Answer: B. 11, 12, 13
Let the three consecutive integers be x, x+1, and x+2. Their sum is 3x + 3 = 36. Solving for x, we get x = 11. Therefore, the integers are 11, 12, and 13.
The length of a rectangle is 5 cm more than its width. If the perimeter is 38 cm, find the length and width.
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Answer: A. Length = 12cm, Width = 7cm
Let the width be x. The length is x + 5. The perimeter is 2(x + x + 5) = 38. Solving for x, we get x = 7 (width). The length is 7 + 5 = 12.
Two angles are supplementary. One angle is 20 degrees more than twice the other. Find the measure of the smaller angle.
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Answer: C. 30
Let one angle be x. The other angle is 2x + 20. Since they are supplementary, x + 2x + 20 = 180. Solving for x, we get x = 30.
The numerator of a fraction is 3 less than the denominator. If 2 is added to both the numerator and the denominator, the new fraction is 2/3. Find the original fraction.
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Answer: D. 4/7
Let the denominator be x. The numerator is x - 3. The equation is (x - 3 + 2)/(x + 2) = 2/3. Solving for x gives x = 7. The original fraction is 4/7.
A boat travels 16 km upstream and 24 km downstream in 6 hours. It travels 36 km upstream and 48 km downstream in 13 hours. Find the speed of the boat in still water and the speed of the current.
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Answer: B. Speed of boat = 10 km/hr, Speed of current = 4 km/hr
Let the speed of the boat in still water be x km/hr and the speed of the current be y km/hr. Upstream speed = x - y, downstream speed = x + y. We have two equations: 16/(x - y) + 24/(x + y) = 6 and 36/(x - y) + 48/(x + y) = 13. Solving these simultaneous equations (using substitution or elimination) gives x = 10 and y = 4.
More questions in this quiz
Answers and explanations are in the full quiz.
- If a number is doubled and then increased by 5, the result is 21. What is the number?
- A father is 3 times as old as his son. In 5 years, the sum of their ages will be 62. Find the son's current age.
- A train travels a distance of 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hour less for the same journey. Find the original speed of the train.
- A man buys a certain number of mangoes at 3 for Rs. 5 and sells them at 5 for Rs. 12. He gains Rs. 75 in the transaction. How many mangoes did he buy?
- A shopkeeper sells two types of sweets, A and B. He sells sweet A at Rs. 2 per piece and sweet B at Rs. 3 per piece. On a particular day he sold 100 sweets in total and made Rs. 240. How many sweets of type A did he sell?
- John and Mary together have 45 marbles. If John has 5 more marbles than Mary, how many marbles does Mary have?
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