Math

Q10. Percentage Increase Problem

A number is first increased by \( x\% \), and then again increased by \( x\% \). The total increase becomes 44%. Find the value of \( x \).

Solution:

Let the original number be \( 100 \).

After the first increase: \[ \text{New number} = 100 + \frac{x}{100} \cdot 100 = 100 + x \] After the second increase: \[ \text{New number} = (100 + x) + \frac{x}{100} \cdot (100 + x) = (100 + x)\left(1 + \frac{x}{100}\right) \] Now simplify: \[ (100 + x)\left(1 + \frac{x}{100}\right) = \left(100 + x\right)\left(\frac{100 + x}{100}\right) = \frac{(100 + x)^2}{100} \] This final value is a 44% increase over the original number (100), so: \[ \frac{(100 + x)^2}{100} = 144 \] Multiply both sides by 100: \[ (100 + x)^2 = 14400 \] Take square root: \[ 100 + x = \sqrt{14400} = 120 \] \[ x = 120 - 100 = \boxed{20} \]

100 mcqs

Percentage MCQs for RI Mains (Only Questions)

Level 1 – Basic (1–20)

1. What is 20% of 150?
2. Find 35% of 240.
3. Convert 3/4 into percentage.
4. A student got 40 marks out of 80. What is the percentage?
5. What percent of 250 is 100?
6. What number is 25% of 200?
7. 60 is what percent of 240?
8. Convert 0.75 into percentage.
9. What is 150% of 60?
10. Find the number whose 40% is 120.
11. Increase 180 by 25%.
12. What is 30% less than 250?
13. What percent is 60 of 300?
14. A number increases from 400 to 500. What is the percent increase?
15. A number decreases from 250 to 200. What is the percent decrease?
16. What is 12.5% of 64?
17. If 15% of a number is 45, what is the number?
18. What percent of ₹400 is ₹88?
19. 10% of a number is 90. Find the number.
20. Find 66⅔% of 120.

Level 2 – Intermediate (21–50)

21. A value increased by 25% and then decreased by 20%. Find net % change.
22. A is 25% more than B. B is what percent less than A?
23. A’s salary is ₹8000, which is 80% of B’s salary. Find B’s salary.
24. 45% of x is equal to 30% of y. What is x : y?
25. A’s marks are 20% more than B’s. If B got 150 marks, how many marks did A get?
26. A man spends 85% of his income. If his income is ₹60,000, how much does he save?
27. A shopkeeper increases the price of an item by 20%. If the cost price was ₹500, what is the new price?
28. An item originally priced ₹100 is sold after a 25% discount. What is the selling price?
29. A man gives 10% of his salary to his son, 20% to his daughter. If salary is ₹50,000, how much remains?
30. The population of a village increases by 10% every year. Find the % increase in 2 years.
31. A’s salary increases by 20% and then again by 10%. Find total % increase.
32. A’s income is 50% more than B’s. B’s income is what % less than A’s?
33. A number is increased by 10% and then decreased by 10%. What is the net change?
34. If 40% of a number is 120, find the number.
35. 25% of A is equal to 30% of B. Find A : B.
36. A salary increases by 15% and then decreases by 15%. Find the net % change.
37. If 10% of A = 15% of B, what is A : B?
38. A spends 75% of his income. If income is ₹48,000, find expenses.
39. The value of a machine depreciates 20% annually. What will be its value after 2 years if original value is ₹50,000?
40. What percent of ₹1200 is ₹360?
41. The price of sugar increases from ₹40 to ₹50. Find the % increase.
42. A person gives 5% of his salary to charity. If he gives ₹1250, find his income.
43. An item is marked 30% above cost price. It is sold at 10% discount. Find the profit %.
44. A student scores 60% in English, 80% in Math. Total marks in both subjects = 300. Find total marks obtained.
45. A person saves 20% of his salary. If he saves ₹8000, what is his salary?
46. A is 40% more than B and B is 25% less than C. A is what % of C?
47. What % increase is needed to change 160 to 200?
48. If the price of petrol rises 25%, how much less petrol can be bought for ₹500?
49. A sells a product at 20% loss. If SP is ₹800, find CP.
50. Successive discounts of 10% and 20% are equal to a single discount of?

... (Continue Level 3 to Level 5 MCQs in similar format) ...