CBSE Class 8 Maths Comparing Quantities HOTs

QUESTION BANK

Question. A trader offers two successive discounts of 10% and 8% on an article whose marked price is ₹ 4,600.
Find its selling price.
Answer: ₹ 3808.80

Question. Which is more favourable to the seller and by how much—₹ 800 with 20% discount or the same amount with successive discounts of 12% and 10%?
Answer: Successive discount of 12% and 10%

Question. Pratap borrowed ₹ 10,000 from a bank at the rate of 10% per annum simple interest and lent it to Gaurav at the same rate of interest per annum compound interest. What will be his gain after 3 years?
Answer: ₹ 310

Question. A sum compounded annually becomes 729/512 times of itself in 3 years. Find the rate of interest per annum.
Answer: 12.5%

Question. Kusum and Ravi borrowed ₹ 80,000 and ₹ 60,000 respectively for a period of 3 years. Kusum paid simple interest at the rate of 20% per annum, while Ravi paid compound interest at the rate of 20% per annum compounded annually. Who paid more interest and by how much?
Answer: Kusum, ₹ 4320

Question. The difference between the simple interest and the compound interest on a certain sum for 2 years at the rate of 10% is ₹ 50. Find the principal.
Answer: ₹ 5000

Question. In how many years will a sum of ` 30,000 amount to ₹ 33,708 at the rate of 6% per annum compounded annually?
Answer: 2 years

Question. A library had 8,000 registered members. The membership increased at the rate of 5% every six months.
After what time will the total membership be 9,261?
Answer: 1.5 years

Question. If the population of a town decreases 6.25% annually and the present population is 20480000, find its population after 3 years.
Answer: 16875000

Question. Sunita paid ₹ 27.50 as sales tax on a bottle of shampoo worth ₹ 250. Find the rate of Sales tax.
Answer: 11%

Question. What price should Kiran mark on a sari which cost her ₹ 3000 so as to gain 20% after allowing a discount of 15%?
Answer: ₹ 10588.23

Question. A piece of elastic was stretched by 24% to a length of 31cm. Find its unstretched original length.
Answer: 25 cm

Question. At what rate percent compound interest, will ₹ 10,000 amount to ₹ 13,310 in 3 years interest being compounded annually? 
Answer: 21%

HOTS

Question. Alka bought an article and spent ₹ 100 on its repairs. She then sold it to Tina at a profit of 20%. After some time Tina sold it back to Alka at a loss of 20%. If Alka gains ` 240, what is the amount for which Alka had bought the article?
Answer: ₹ 5900

Question. A dealer comes from Mathura to Delhi to buy an article which costs 12% less in Delhi than in Mathura.
His expenses are ₹ 240 and he makes a profit of ₹ 300 on selling the article in Mathura. What did the article cost in Mathura? What is his profit percent?
Answer: ₹ 2500, 10.94%

Question. A sum of money amounts to ₹ 1,210 in 2 years and to ₹ 1,610.51 in 5 years. Find the principal and the rate of interest when interest is compounded annually.
Answer: ₹ 1000, 10%

Question. A farmer borrowed ₹ 12,800 from a moneylender to install a Jet pump. The rate of interest is 11(1/4)% per annum compounded annually. At the end of 2 years, the farmer cleared the loan by paying ₹ 10,842 and a gold ring. Find the cost of the ring.
Answer: ₹ 5000

Question. A certain sum of money is invested at the rate of 10% per annum compound interest, compounded annually. If the difference between the interests of the third year and the first year is ₹ 1,155, find the sum invested.
Answer: ₹ 55000

Question. A builder employed 4000 workers to work on a project. At the end of the first year, 10% of the workers were removed, at the end of the second year 5% of those working at that time were retrenched. But to complete the project in time, number of workers was increased by 15% at the end of the third year. How many workers were working during the fourth year?
Answer: ₹ 3933

CHALLENGES

1. In a school, 30% of students play chess, 60% play carrom and the rest play other games. If the total number of students in the school is 900, find the exact number of students who play each game.

2. In a school function ₹ 360 remained after spending 82% of the money. How much money was there in the beginning? Verify your answer.

3. Akshay's income is 20% less than that of Ajay. What percent is Ajay's income more than that of Akshay?

4. A daily wage employee spends 84% of his weekly earning. If he saves ₹ 384, find his weekly earning.

5. A factory announces a bonus of 10% for its employees. If an employee gets ₹ 6,078 as bonus, find his actual salary.

6. A time interval of 3 minutes and 20 seconds is wrongly calculated as 3 minutes and 25 seconds. What is the percentage error?

7. Hari reads 22% of the pages of a book on the first day, 53% on the second day and 15% on the third day. If the number of pages remaining to be read is 30, find the total number of pages in the book.

8. If 60 ml of water contains 12% of chlorine, how much water must be added in order to create an 8% chlorine solution?

9. Praveen has ₹ 30 more than Peter. They plan to go to a mall. Praveen's mother gives him a 20% bonus; and Peter's father gives him a 44% bonus. If they now have the same amount of money, how much did they each start with?

10. A TV set costing ₹ 48,000 was put on sale with 30% off. It wasn't sold, so the price was lowered. After an additional discount the new price was ₹ 28560. What was the second percent discount that was given?

11. Raju's salary increased from ₹ 20000 to ₹ 22000 per month after his first evaluation. After his second evaluation his pay was raised further to ₹ 24400. When comparing the percentage increases, what percent more than the first raise was the second?

12. The price of cooking oil has increased by 22%. A family reduces its oil consumption in order to be unaffected by the increase in the price of the oil. How much percentage it must reduce its oil consumption?

13. Two numbers are less than the third number by 30% and 37%, respectively. How much percent is the second number less than the first?

14. In a mixture of 60 litres, the ratio of milk to water is 2 : 1. If we want to make it 1 : 2, what percentage of water should be added to the mixture?

15. A garment owner purchased shirts at a price of ₹ 350 each. He wanted to get a profit of 20% on it.
But in order to attract customers, he wanted to show that he is offering a discount of 25%. So he increased the price by 45% and then set a discount of 25%. What is the percentage profit he gets on each shirt?

16. A man spends 75% of his income. His income is increased by 20% and he increased his expenditure by 10%. How much is the percentage increase in his savings?

17. It is known that 5% of the income of A is equal to 15% of that of B and 10% of the income of B is equal to 20% of that of C. If A, B, C together earn ₹ 1,80,000, find their respective incomes.

18. A man invests ₹ 5,000 for 2 years at compound interest. After one year, his money amounts to ₹ 5,150.
Find the interest for the second year.

19. Find the amount on ₹ 10,000 after 2 years if the rates of interest are 3% and 4% for successive years.

20. Prahlad invests a sum of money in a bank and gets ₹ 3307.5 and ₹ 3472.87 in the 2nd and 3rd year respectively. Find the sum he invested.

21. On what sum of money will the difference between the simple interest and compound interest for 2 years at 4% per annum be equal to ₹ 100? (Hint: Assuming the principal to be ` 100, first calculate the SI and CI, then proceed.)

22. A sum of money is invested at compound interest payable annually. The interest in two successive years is ₹ 275 and ₹ 300. Find the rate of interest.

23. The difference between the compound interest and the simple interest on a certain sum for 2 years at 7(1)/2% per annum is ₹ 360. Find the sum. Verify your answer.

24. Teju invests ₹ 12,000 at 5% interest compounded annually. If he receives an amount of ₹ 13,320 at the end, find the period.

25. The present population of a village is 18,000. It is estimated that the population of the village grows by 3% per year. Find the population of the village after 4 years.

26. Jeshu purchased a bike by paying ₹ 52,000. If the value depreciates by 2% every year, find the value of the bike after 3 years.

27. The difference between the simple interest and the compound interest on a certain principal for 2 years is ₹ 160. If the simple interest is ₹ 2,880, find the rate of interest.

28. A sum amounts to ₹ 2,916 in 2 years and ₹ 3,194.28 in 3 years when compounded annually. Find the principal.

29. A sum of ₹ 5,500 was taken as loan. This is to be paid back in two equal instalments. If the rate of interest is 20% per annum compounded annually, find the value of each instalment.

30. What is the compound interest on ₹ 5,000 for 3 years at 8% for the first year, 10% for the second year and 12% for the third year?

31. Find the minimum number of complete years in which a sum of money put at 20% compound interest will be more than doubled.

SUMMARY

1. Percentage refers to a fraction with 100 as its denominator.

2. Cost price is written as CP and selling price as SP, then
a. Profit=SP–CP, if SP>CP
b. Loss=CP–SP, if CP>SP

3. To find the actual CP of an article, overhead expenses are added to the price at which the article was purchased.

4. Discount is given on the marked price and is normally announced in the percentage form.

5. MP - Discount = SP for the seller = CP for the customer.

6. Discount % =Discount/MP x 100%

7. SP = MP x [100 - Discount%/MP]

8. MP= 100 x SP/100 - Discount%

9. In case of C.I., principal for a particular year = amount of the previous year.

10. If the conversion period is 1 year, the interest is said to be compounded annually.

11. If the interest is compounded annually
A = P [1+r/100]^-n

12. For compounding interest half yearly, half the rate % and double the time period. 
A = P (1+r/2/100)²ⁿ (where n=number of years)

13. For compounding interest quarterly, the rate% is made one-fourth and time period is made four times. 
A = P (1+r/4/100)⁴ⁿ

14. The relative increase in the value of a thing or an asset is called appreciation and the appreciation per unit time is called the rate of appreciation.

15. The relative decrease in the value of a thing or a commodity is called depreciation and the depreciation per unit time is called the rate of depreciation. 

ERRORANALYSIS

1. Students often make mistake while calculating profit % and loss% (They calculate these on SP in place of CP).

2. Students calculate discount on SP when MP is not given.

3. Incorrect rate and time period is taken by students when compounding is not done annually.

4. Wrong assumption of initial and final value is done while doing questions of growth and depreciation.

ACTIVITY I

Aim : To estimate the number of periods required to double an original investment.
Theory : The "Rule of 72" is a simplified way to determine how long an investment will take to double, given a fixed annual rate of return.
It is an approximate estimation of number of years it will take for an investment to double.
Example : The "Rule of 72" states that a sum of money (say ` 10,000) invested at 10% would take 7.2years (= 71/10) to turn into ₹ 20,000. In reality, a 10% investment will take 7.3 years to double.

How it works : Divide 72 by the rate of interest to calculate the time an investment takes to double itself. 

ACTIVITY II

Group Project

You have ₹ 50,000 which you wish to deposit in a bank. Divide the class into four groups. Each group should go to one of the given banks and find out their rate of interest to complete the table:
• Punjab National Bank • State Bank of India

• ICICI Bank • HDFC Bank 
Which bank will give more money at the end of 5 years assuming that you do not make any additional deposits or withdrawals?