Percentages and exponential change

1. Find 18% of 350.

Answer B: 63

18% of 350 is 0.18 × 350 = 63. A mental check gives 10% = 35 and 8% = 28, so their sum is 63.

2. Express 84 as a percentage of 120.

Answer B: 70%

The required comparison is (84/120) × 100% = 0.7 × 100% = 70%. Checking forward, 70% of 120 is 84.

3. Express 96 as a percentage of 80.

Answer C: 120%

Calculate (96/80) × 100% = 1.2 × 100% = 120%. This means 96 is 20% greater than the reference value 80.

4. Increase MVR 640 by 12.5%.

Answer C: MVR 720

The new amount is 640 × 1.125 = MVR 720. Equivalently, 12.5% is one eighth, and one eighth of 640 is MVR 80.

5. Decrease MVR 1250 by 18%.

Answer B: MVR 1025

Use multiplier 0.82: 1250 × 0.82 = MVR 1025. The reduction is MVR 225, and 1250 − 225 confirms the result.

6. Which multiplier represents a decrease of 7%?

Answer B: 0.93

After a 7% decrease, 100% − 7% = 93% remains. As a decimal, 93% is 0.93, so this is the correct multiplier.

7. A quantity rises from 480 to 600. What is the percentage increase?

Answer B: 25%

The increase is 600 − 480 = 120. Dividing by the original gives 120/480 = 0.25, so the percentage increase is 25%.

8. A price falls from MVR 840 to MVR 714. What is the percentage decrease?

Answer B: 15%

The reduction is 840 − 714 = MVR 126. Then 126/840 × 100% = 15%, so the price decreased by 15%.

9. An item costs MVR 240 and sells for MVR 294. What is the profit percentage on cost?

Answer C: 22.5%

Profit is 294 − 240 = MVR 54. Measured against cost, 54/240 × 100% = 22.5%, which answers the stated question.

10. An item costing MVR 600 is sold for MVR 540. What is the loss percentage on cost?

Answer B: 10%

Loss = 600 − 540 = MVR 60. The loss percentage is 60/600 × 100% = 10%; the selling price is therefore 90% of cost.

11. A bag costs MVR 384 after a 20% discount. What was its original price?

Answer B: MVR 480

A 20% discount leaves multiplier 0.80. The original price is 384 ÷ 0.80 = MVR 480, and 20% off 480 gives 384.

12. After a 15% increase, a fee is MVR 690. What was the fee before the increase?

Answer B: MVR 600

The original fee is 690 ÷ 1.15 = MVR 600. A forward check gives 15% of 600 = 90 and 600 + 90 = 690.

13. A trader sells an item for MVR 672 after making a 12% profit on cost. Find the cost price.

Answer B: MVR 600

Cost price = 672 ÷ 1.12 = MVR 600. The profit is 12% of 600 = MVR 72, giving selling price MVR 672.

14. A population is 325 after a 35% decrease. What was the original population?

Answer C: 500

The remaining population is 65% of the original. Dividing gives 325 ÷ 0.65 = 500, and 65% of 500 is 325.

15. Find the simple interest on MVR 2500 at 6.4% per year for 3 years.

Answer C: MVR 480

Simple interest = 2500 × 0.064 × 3 = MVR 480. The final amount would be MVR 2980, but the question asks only for interest.

16. MVR 1800 earns 4.5% simple interest per year for 5 years. What is the final amount?

Answer D: MVR 2205

Interest = 1800 × 0.045 × 5 = MVR 405. Adding the principal gives a final amount of 1800 + 405 = MVR 2205.

17. MVR 2000 is invested at 5% compound interest per year for 3 years. Find the final amount.

Answer C: MVR 2315.25

The amount is 2000 × 1.05^3 = MVR 2315.25. MVR 2300 is the simple-interest result and omits interest on earlier interest.

18. For MVR 1000 invested at 10% per year for 2 years, how much more interest does annual compound interest earn than simple interest?

Answer B: MVR 10

Compound amount is MVR 1210 and simple amount is MVR 1200. Their interest differs by MVR 10 because year two compounds the first MVR 100 interest.

19. A population of 12 500 grows by 4% each year. What is the population after 2 years according to this model?

Answer C: 13 520

The model gives 12 500 × 1.04^2 = 13 520. Adding 8% of the original would give 13 500 and miss growth on the first year's increase.

20. A culture starts with 320 cells and doubles at the end of each hour. How many cells are modelled after 3 hours?

Answer D: 2560

The model is 320 × 2^3 = 320 × 8 = 2560 cells. The values after each hour are 640, 1280 and then 2560.

21. A vehicle worth MVR 28 000 depreciates by 15% each year. What is its value after 2 years?

Answer B: MVR 20 230

The value is 28 000 × 0.85^2 = MVR 20 230. Subtracting 30% of the original would give MVR 19 600 and would not model repeated depreciation.

22. A quantity of 6400 decreases by 30% in each period. What remains after 3 periods?

Answer D: 2195.2

The remaining quantity is 6400 × 0.70^3 = 2195.2. Subtracting 90% of the original would incorrectly use a constant absolute decrease.

23. A value of 1000 increases by 20% and then decreases by 20%. What is the final value?

Answer B: 960

The final value is 1000 × 1.20 × 0.80 = 960. Equal percentage increase and decrease do not cancel because the second change acts on 1200.

24. Which expression models an initial population of 80 000 decreasing by 1.5% per year for n years?

Answer B: 80 000(0.985)^n

A 1.5% decrease leaves 98.5% each year, so the repeated multiplier is 0.985. After n years the model is 80 000(0.985)^n.