Finding sales tax the cost sofa set ship was

Percentage, Profit and Loss (Simple interest and compound interest)

Subtopics
• Direct & Reverse Variation
• Profit & Loss
• Simple Interest & Compound Interest

Direct Variation: Two quantities are said to vary directly if the increase (or decrease) in one quantity causes the increase (or decrease) in the other quantity.

Illustration 2. If Rs. 166.50 is the cost of 9 kg of sugar, how much sugar can be purchased for Rs. 259?

Sol.: For Rs. 166.50, sugar purchased = 9kg

Hence Vineeta got 45 marks.

Inverse Variation: Two quantities are said to vary inversely if the increase (or decrease) in one quantity causes the decrease (or increase) in the other quantity
Illustration 4. (i) The time taken to finish a piece of work varies inversely as the number of men at work.

Thus a per cent can be expressed as a fraction with 100 as denominator.

Thus a decimal number can be expressed as a per cent.

Illustration 7. A number is increased by 20% and then decreased by 20%. Find the net increase or decrease per cent.

Sol.: Let the number = 100
∴ Number after 20% increase = 100 + 20 = 120 Decrease in the new number = 20% of 120

20% increase means
Rs. 100 increased to Rs. 120.

So, Rs. 34,000 will increase to?

Marked Price:
In big shops and departmental stores, every article is tagged with a card and its price is written on it. This is called the marked price of that article, abbreviated as MP.

List Price:
Items which are manufactured in a factory are marked with a price according to the list supplied by the factory, at which the retailer is supposed to sell them. This price is known as the list price of the article.

Illustration 10. A trader marks his goods at 40% above the cost price and allows a discount of 25%. What is his gain per cent?

Sol.: Let the cost price be Rs. 100.

Cost Price (CP): The amount for which an article is bought is called its cost price.

Selling Price (SP): The amount for which an article is sold is called its selling price.

Since (SP) > (CP), Mohit makes a gain.

Gain = Rs. Rs. (875 – 750) = 125.

Illustration 13. Rahul purchased a table for Rs. 1260 and due to some scratches on its top he had to sell it for Rs. 1197. Find his loss per cent.

Sol.: CP = Rs. 1260 and SP = Rs. 1197.
Since (SP) < (CP), Rahul makes a loss.

OVERHEADS: Sometimes, after purchasing an article, we have to pay some more money for things like transportation, labour charges, preparing charges, local taxes, etc. For calculating the total cost price, we add overheads to the purchase price.

These days however, the prices include the tax known as Value Added Tax (VAT).

Illustration 15. (Finding Sales Tax) the cost of a sofa set at a ship was Rs. 9000. The sales tax charged was 5%. Find the bill amount.

Illustration 16. Value Added Tax (VAT) A man bought an air cooler for Rs. 5500 including a tax of 10%. Find the price of the air cooler before VAT was added.

Interest : The additional money paid by the borrower in lieu of the money used by him is called interest. Amount : The total money paid back to the lender is called amount.

Amount = Principal + Interest
Rate : Interest on Rs. 100 for 1 year is called rate per cent per annum (abbreviated as rate % p.a.) Thus, if rate = 9% per annum, then it means that the interest on Rs. 100 for 1 year is Rs. 9.

Amount at the end of the third year ∴ compound interest

= Rs. (28090 + 1685.40) = Rs. 29775.40 = Rs. (29775.40 – 25000) = Rs. 4775.40.

If difference in S.I. is Rs. 100, then principal

Case 1: When the interest is compounded annually

Let principal = Rs P, rate = R% per annum and time = n years.

Illustration 19. Find the amount of Rs. 8000 for 3 years, compounded annually at 5% per annum. Also. find the compound interest.

Illustration 21. Find the amount of Rs. 12000 after 2 years, compounded annually; the rate of interest being5% p.a. during the first year and 6% p.a. during the second year. Also, find the compound interest,
Sol.: Here, P = Rs. 12000, p = 5% p.a. and q = 6% p.a.

Hence, compound interest = Rs. (38637 – 31250) = Rs. 7387. INTEREST COMPOUNDED HALF-YEARLY Let principal = Rs. P, rate = R% per annum, time = n years. Suppose that the interest is compounded half-yearly.

Compound interest = (amount) – (principal).

Sol.: Here, principal = Rs. 160000, rate = 10% per annum = 5% per half-year, time = 2 years = 4 half- years.

INTEREST COMPOUNDED QUARTERLY Let principal = Rs. P, rate = R% per annum , time = n years. Suppose that the interest in compounded quarterly.

time = 9 months = 3 quarters.

per quarter = 2% per quarter,

You must have seen a child at the time of his (her) birth, after six months, one year or two years. Have you observed any change? The change may be in weight or height. This is called growth. If you observe a plant, you cannot see its growth in a day or two but the growth may be visible in a month or two. This is an example of a positive growth.

Now let us take an example of a car. Suppose the price of a new car is Rs. 215000. Will you get the same price of this car after using it for 2 years? No, because the price of an old car is always less then the price

Sol.: Present value = Rs. 100000
Rate of depreciation = Rs. 10%

= Rs. 81000.

(ii) amount after n years (compounded half-yearly)

FORMULA

vi. To find CP when SP and gain% or loss% are given:

How much interest did he get at the expiry of the period?

paid Rs 512.50 as compound interest, what sum did he borrow?

7. The population of a town was 160000 two years ago. If it hand increased by 3% and 5%

11. Simple interest on a certain sum of money for 2 years at 6 1 2% per annum is Rs. 5200. What will

be the compound interest on that sum at the same rate and for the same period?

3. A sum of money doubles itself in 10 years at a simple interest. What is the rate of interest?

4. The simple interest on a sum money is 1 9 of the principal, and the number of years is equal to the rate per cent per annum. Find the rate per cent.

8. A grocer sells at a profit of 10% and uses a weight which is 20% less. Find his total percentage gain.

9. If simple interest on Rs 2000 increases by Rs 40, when the rate % increases by 2% per annum. Find the time.

sold it for Rs 1680. Find his profit or loss. What was his profit or loss percent?

(A) Rs 960 (B) Rs 1060
(C) Rs 1200 (D) 920
7. The profit earned by selling an article for Rs 482 is equal to loss incurred when the same article is solid for Rs 318. What should be the sale price of the article for making 30 per cent profit?

(A) Rs 870 (B) Rs 890
(C) Rs 880 (D) Rs 990
11. A reduction of 10% in the price of slat enables a person to buy 2 kg more for Rs 18. Find the reduced and the original price per kg of salt respectively.

(A) Re 1, Rs 0,9 (B) Rs 0.9, Re 1
(C) Rs 2, Rs 1.9 (D) Rs 1.9, Rs 2
12. A reduction of 10 per cent in the price of potatoes enables me to obtain 25 kg more for Rs 225. What is the reduced price per kg? Find also the price per kg.

the original price per kg of tea.

the original price per kg of coffee.

(A) Rs. 217 11 (B) Rs. 11 317

(A) cost price of A 24 is (C) sells price of B 20 is

(B) cost price of B 25.2 is
(D) cost price of B 20 is

statement in Column I can have correct matching with ONE OR MORE statement(s) in

column II.

22. A reduction of 20% in the price of mangoes enables a person to purchase 12 move for Rs. 15. what was the price of 16 mangoes before reduction?

23. A certain sum of money amounts to Rs. 550 in 3 years and to Rs. 650 in 4 years. if Rs. 246 is subtracted from the sum then what amount is left?.

. Rita invests Rs. 93750 at 9.6% per annum for 3 years and the interest is compounded annually. Calculate

(ii) the amount outstanding to her at the end of second year,

(A) 112164 (B) 112614 (C) 112620 (D) 112641

Answer key

Assignment - 1

14. 5% 15. Rs 408

Assignment - 2

Competition Corner

Straight Objective Question

16. (A, B) 17. (A, C) 18. (A, B)

Matrix Match

26. Comprehension Type

i. (C) ii. (D) iii. (B)

5. (C)
10. (C)
15. (B)

25. (4)

= Rs. 1100
Amount at the end of 2nd year = Rs. (11000 + 1100) = Rs. 12100

= Rs. 1210

∴ Amount at the end of 3rd year = Rs. (12100 + 1210) = Rs. 13310. Sol. 3 Principal = Rs. 32000
Time = 3 years
Rate = 12.5% per annum