Collection of math questions: 1. Cost of a bus decreased from 18 lakh to 15.5 lakh, find the percentage decrease. 2. Convert the following to percentage: (a) 0.008, (b) 34/117, (c... Collection of math questions: 1. Cost of a bus decreased from 18 lakh to 15.5 lakh, find the percentage decrease. 2. Convert the following to percentage: (a) 0.008, (b) 34/117, (c) 12.005, (d) 40 3. Price of a pen is increased from Rs 20 to Rs 21. Find the percentage increased. 4. At what rate a sum of money become doubled itself in 10 years. 5. At what rate percent a sum of money become triple of itself in 15 years. 6. Find the simple interest if Rs 1897 are invested for 1 year and 8 months at 2(5/6)% annually. 7. In how many years will a sum of money doubled itself at 10% simple interest per annum? 8. If a certain principal amount to Rs 44,000 at 5% p.a. over 2 years, how much will it amount to in 3 years at the same rate? 9. If Rs 750 amount to Rs 885 in three years at simple interest, find the rate of interest. 10. The cost price of 24 articles is the selling price of 15 articles. Find the gain percentage. 11. By selling a pen for Rs 165, Mukti gain 10%. If she had sold it for Rs 157.50, What percentage Would she have loss or gain? 12. Express 1:8 as per cent. 13. The selling price of 10 pencils is equal to the cost price of 11 pencils. What is the profit percent? 14. The strength of a high school is 2500 out of this 600 are in pre-primary section, 800 in primary section, 700 in middle section and the remaining are in high school. Find the percentage of students in each section. 15. Rohan purchase a book by Rs.356 and due to some personal reason sold it by Rs, 267, find the profit or loss percent. Read more

Steps to Solve

1. Q1: Calculate the amount of decrease

Calculate the difference between the original cost and the decreased cost. $ \text{Decrease} = 18 \text{ lakh} - 15.5 \text{ lakh} = 2.5 \text{ lakh} $

2. Q1: Calculate the percentage decrease

Divide the decrease by the original cost and multiply by 100.

$ \text{Percentage Decrease} = \frac{2.5}{18} \times 100 = \frac{250}{18} = \frac{125}{9} = 13\frac{8}{9}% $

3. Q2(a): Convert 0.008 to percentage

Multiply the decimal by 100.

$ 0.008 \times 100 = 0.8% $

4. Q2(b): Convert 34/117 to percentage

Divide 34 by 117 and multiply by 100.

$ \frac{34}{117} \times 100 \approx 29.06% $

5. Q2(c): Convert 12.005 to percentage

Multiply the decimal by 100.

$ 12.005 \times 100 = 1200.5% $

6. Q2(d): Convert 40 to percentage

Multiply the number by 100.

$ 40 \times 100 = 4000% $

7. Q3: Calculate the amount of increase

Calculate the difference between the increased price and the original price.

$ \text{Increase} = 21 - 20 = 1 $

8. Q3: Calculate the percentage increase

Divide the increase by the original price and multiply by 100.

$ \text{Percentage Increase} = \frac{1}{20} \times 100 = 5% $

9. Q4: Determine the rate for doubling in 10 years

Let P be the principal amount and R be the rate of interest. The amount becomes 2P in 10 years. Using the simple interest formula: $ \text{Simple Interest} = \frac{P \times R \times T}{100} $ Since the amount doubled, the simple interest is equal to the principal, P. $ P = \frac{P \times R \times 10}{100} $ $ 1 = \frac{R \times 10}{100} $ $ R = \frac{100}{10} = 10% $

10. Q5: Determine the rate for tripling in 15 years

Let P be the principal amount and R be the rate of interest. The amount becomes 3P in 15 years. This means the simple interest earned is 2P.

$ 2P = \frac{P \times R \times 15}{100} $ $ 2 = \frac{R \times 15}{100} $ $ R = \frac{200}{15} = \frac{40}{3} = 13\frac{1}{3}% $

11. Q6: Calculate the simple interest

Principal (P) = Rs 1897 Time (T) = 1 year and 8 months = $1 + \frac{8}{12} = 1 + \frac{2}{3} = \frac{5}{3}$ years Rate (R) = $2\frac{5}{6} = \frac{17}{6}%$

$ \text{Simple Interest} = \frac{P \times R \times T}{100} = \frac{1897 \times \frac{17}{6} \times \frac{5}{3}}{100} = \frac{1897 \times 17 \times 5}{100 \times 6 \times 3} = \frac{161245}{1800} \approx 89.58 $

12. Q7: Calculate the number of years for doubling at 10% simple interest

Let P be the principal amount. The amount becomes 2P. This means the simple interest earned is P. Rate (R) = 10% $ P = \frac{P \times 10 \times T}{100} $ $ 1 = \frac{10 \times T}{100} $ $ T = \frac{100}{10} = 10 \text{ years} $

13. Q8: Calculate the amount after 3 years

Let the principal be P. Amount after 2 years is Rs 44,000 at 5% p.a. $ 44000 = P + \frac{P \times 5 \times 2}{100} = P + \frac{10P}{100} = P + 0.1P = 1.1P $ $ P = \frac{44000}{1.1} = 40000 $ Amount after 3 years: $ A = 40000 + \frac{40000 \times 5 \times 3}{100} = 40000 + \frac{600000}{100} = 40000 + 6000 = 46000 $

14. Q9: Calculate the rate of interest

Principal (P) = Rs 750 Amount (A) = Rs 885 Time (T) = 3 years Simple Interest = A - P = 885 - 750 = 135 $ \text{Simple Interest} = \frac{P \times R \times T}{100} $ $ 135 = \frac{750 \times R \times 3}{100} $ $ 13500 = 750 \times 3 \times R $ $ R = \frac{13500}{750 \times 3} = \frac{13500}{2250} = 6% $

15. Q10: Calculate the gain percentage

Let the cost price of one article be $x$.

Cost price of 24 articles = $24x$ Selling price of 15 articles = $24x$ Selling price of one article = $\frac{24x}{15} = \frac{8x}{5}$

Profit = Selling price - Cost price = $\frac{8x}{5} - x = \frac{3x}{5}$ Profit percentage = $\frac{\text{Profit}}{\text{Cost Price}} \times 100 = \frac{\frac{3x}{5}}{x} \times 100 = \frac{3}{5} \times 100 = 60%$

16. Q11: Calculate the gain/loss percentage if sold for Rs 157.50

Selling price = Rs 165, Gain = 10% Cost price = $\frac{100}{100 + \text{Gain}%} \times \text{Selling Price} = \frac{100}{110} \times 165 = \frac{10}{11} \times 165 = 10 \times 15 = 150$ New selling price = Rs 157.50 Profit = 157.50 - 150 = 7.50 Profit percentage = $\frac{7.50}{150} \times 100 = \frac{750}{150} = 5%$

17. Q12: Express 1:8 as a percentage

$ \frac{1}{8} \times 100 = \frac{100}{8} = \frac{25}{2} = 12.5% $

18. Q13: Calculate the profit percentage

Let the cost price of one pencil be $x$. Selling price of 10 pencils = Cost price of 11 pencils = $11x$ Selling price of one pencil = $\frac{11x}{10}$ Profit = Selling price - Cost price = $\frac{11x}{10} - x = \frac{x}{10}$ Profit percentage = $\frac{\text{Profit}}{\text{Cost Price}} \times 100 = \frac{\frac{x}{10}}{x} \times 100 = \frac{1}{10} \times 100 = 10%$

19. Q14: Calculate the percentage of students in each section

Total strength = 2500 Pre-primary = 600 Primary = 800 Middle = 700 High school = 2500 - (600 + 800 + 700) = 2500 - 2100 = 400

Percentages: Pre-primary: $\frac{600}{2500} \times 100 = 24%$ Primary: $\frac{800}{2500} \times 100 = 32%$ Middle: $\frac{700}{2500} \times 100 = 28%$ High school: $\frac{400}{2500} \times 100 = 16%$

20. Q15: Calculate the profit or loss percent

Cost price = Rs 356 Selling price = Rs 267 Loss = 356 - 267 = 89 Loss percentage = $\frac{89}{356} \times 100 = 25%$