Q1. If a rectangle has a length of 3x and a width of 2x, what is its area?
Solution:
Area = Length × Width = 3x × 2x = 6x^2.
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Q2. Solve for x: 2x - 4 = 10.
Solution:
2x - 4 = 10. Add 4 to both sides: 2x = 14. Divide by 2: x = 7.
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Q3. A rectangle has a length that is 3 times its width. If the perimeter of the rectangle is 48 cm, what is the width?
Solution:
Let the width be w cm. Then the length is 3w cm. The perimeter is given by: 2(length + width) = 48. Thus, 2(3w + w) = 48. Simplifying gives 8w = 48, so w = 6 cm.
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Q4. A train travels 60 km at a certain speed and returns at 90 km/h. If the total time for the journey is 4 hours, what is the speed of the train on the way to the destination?
Solution:
Let the speed of the train on the way to the destination be x km/h. The time taken to travel to the destination is 60/x hours and the time taken to return is 60/90 hours. The total time is given by: 60/x + 60/90 = 4. Solving for x gives x = 40 km/h.
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Q5. If 5 times a number decreased by 3 equals 12, what is the number?
Solution:
Let the number be x. The equation is: 5x - 3 = 12. Adding 3 to both sides gives 5x = 15, so x = 3.
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Q6. A number is increased by 25% and then decreased by 20%. If the final result is 96, what was the original number?
Solution:
Let the original number be x. The equation is: x * 1.25 * 0.8 = 96. Simplifying gives x = 96 / 1 = 120, so the original number is 100.
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Q7. If a rectangle has a length of (x + 2) and a width of (x - 3), what is the area?
Q8. A school has a total of 300 students. If the ratio of boys to girls is 3:2, how many girls are there?
Solution:
Let the number of boys be 3x and the number of girls be 2x. Then, 3x + 2x = 300. This gives 5x = 300, so x = 60. Therefore, the number of girls is 2x = 120.
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Q9. Solve for y: 2y - 4 = 10.
Solution:
2y - 4 = 10. Add 4 to both sides: 2y = 14. Divide by 2: y = 7.
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Q10. If 5x + 2y = 20 and y = 2, what is the value of x?
Solution:
Substitute y = 2 into 5x + 2(2) = 20. This gives 5x + 4 = 20. Subtract 4: 5x = 16. Divide by 5: x = 16/5 = 3.2.
