Business Mathematics

Compound Interest

When interest is Compounded Annually but Rates being Different for Different years.

Supposed Principal = Rs P, Time = 2 Years and rates of interest be a% and b% for year and second year respectively.

Then, amount after 2 years = Rs [P(1+ a/100) (1 + b/100)]

This formula may similarly be extended for any number of years.

Example:- Find the amount of Rs 16500 for 2 years compounded annually, the rate of interest being

10% for first year and 12% for the second year

Solution.

Here, P = Rs 16500, a = 10% p.a. and b = 12% p.a.

... Amount after 2 years = P (1 +a/100) (1 + b/100)

= Rs [16500 × (1 + 10/100) × (1 + 12/100)]

= Rs (16500 × 11/10 × 28/25) = Rs 20328

Compounded Interest Annually for Time being Fractional

When interest is Compounded Annually, but Time being a Fraction, say 2,3/5 Years.

In this case,

Amount = P(1 + R/100)2 (1 + 3/5 × R/100)

Example:- Find the compound interest on Rs 16000 at 15% per annum 2,1/3 years.

Solution.

Amount after 2,1/3 years

= Rs[16000 × (1 + 15/100)2 × (1 + 1/3× 15/100)]

= Rs(16000 × 23/20 × 23/20 × 21/20) = Rs 22218

... Compound Interest = Rs (22218 – 16000) = Rs 6218

Solve the Questions for Compound Interest

1. Find the amount of Rs 6250 at 8% per annum compound interest for 2 years. Also, calculate the

compound interest?

2. Calculate the compound interest on Rs 14500 at 10% per annum for 3 years/

3. Mohan Lal took a loan of Rs 25600 from a bank to renovate his house. If the rate of interest be

13,3/4% per annum, find the compound interest, he will pay after 2years?

4. A farmer obtained a loan of Rs 12800 from Vijaya bank for buying a tractor. If the bank charges

compound interest at 7,1/2% per annum, what amount he will have to pay after 3 years?

Profit and Loss

INTRODUCTION

A shopkeeper buys goods either form a factory or through a wholesaler. He then sells these articles to his customers.

Usually, a shopkeeper sells an article at a price higher than the price at which he buys it. In such cases, he makes a profit or gain.

Example:- Suppose a shopkeeper buys a umbrella for Rs 200 and sells it for Rs 250. Clearly, he has a profit of Rs 50 in this transaction.

Sometimes, the items purchased by a shopkeeper are defective or they become outdated. In such circumstances, he is forced to sell them even at a price lower than the price at which they are purchased. In such eases, the shopkeeper suffers a loss.

Example:- Suppose a shopkeeper buys a pair of socks for Rs 25 and sells it for Rs 20. Clearly, he has a loss of Rs 5 in this transaction.

Cost Price

The price at which an article is purchased is called its cost price. In short, we write it as C.P.

Selling Price

The price at which an article is sold is called its selling price. In short, we write it as S.P.

Profit or Gain

If S.P. is more than the C.P., then the seller has a profit or gain

Profit = (S.P.) – (C.P.)

Loss

If S.P. is less than the C.P., then the seller incurs a loss

Loss = (C.P.) – (S.P)

Profit or Loss Calculated C.p.

Profit or Loss is Always Calculated on C.P.

Profit on Rs 100 is called Profit %

Profit % = (Profit/C.P. × 100) %

Loss on Rs 100 is called Loss %

Relation between S.p. and C.p.

(i) When an article is sold at r% gain, then:

S.P. = (100 + r) % of C.P.

S.P. (100 + r/100) × C.P.

(ii) When an article is sold at r% loss, then:

S.P. = (100 – r) % of C.P.

S.P. (100 – r/100) × C.P.

From the above two results, we get:

(iii)

C.P. 100/ (100 + r) × S.P., in case of r % gain.

(iv)

C.P. 100/(100 – r) S.P., in case of r % loss

Remark.

(i) If an article is sold at a gain of 25%, then S.P. = 125% of C.P.

(ii) If an article is sold at a loss of 20%, then S.P. = 80% of C.P.

Gross Profit (income)

The total profit (income) without deducting tax is called gross profit (income).

Net Profit (Income)

The profit (income) after deducting tax is called net profit (income)

Note:- When C.P. and S.P. are given for different number of articles, we find the C.P. as well as S.P.

of an equal number of articles (usually, one) and then calculate profit or loss.

Overhead Expenses

Sometimes, apart form paying the cost of an article, a shopkeeper has to spend money on transportation, labour, repair, etc. Such expenses are known as overhead expenses.

Actual C.P. of an article = Cost of the article + Overhead Expenses

Examples

Example1. A man buys an article for Rs 78 and sells it for Rs 89.70. Find his profit his profit per cent.

Solution

C.P. = Rs 78, S.P. = Rs 89.70

... Profit = (S.P.) – (C.P.)

= Rs (89.70 – 78) = Rs 11.70

... Profit % = (11.70/78 × 100) % = 15%

Example2. A watch is bought Rs 875 and sold for Rs 717.50. Find the lose per cent.

Solution.

C.P. = Rs 875, S.P. = Rs 717.50

... Loss = (C.P.) – (S.P.)

= Rs (875 – 171.50) = Rs 157.50

... Loss % = (157.50/875 × 100) % = 18%

Example3. A T.V. and a VCR were sold for Rs 19800 each. The TV was sold at a loss of 10% whereas the VCR at a gain of 10%. Find the gain or loss per cent in the whole transaction.

Solution.

S.P. of TV = Rs 19800, Loss % = 10%

... C.P. = 100/(100 – r) × S.P., where r = 10

= [(100/(100 – 10) × 19800] = Rs (100/90 × 19800) = Rs 22000

S.P. of VCR = Rs19800, Gain % = 10%

... C.P. = 100/(100 + r) × S.P., where r = 10

= Rs[100/(100 + 10) × 19800] = (100/110 × 19800) = Rs 18000

Total C.P. of TV ad VCR = Rs (22000 + 18000) = Rs 40000

Total S.P. of TV and VCR = Rs(2 × 19800) = Rs 39600

... Loss = (C.P.) – (S.P.)

= Rs (40000 – 39600) = Rs 400

Loss % = (400/40000 × 100) % = 1%

Hence, there was a loss of 1% in the whole transaction.

Solve the Question for Profit and Loss

1. Find the profit or loss per cent, when:

(i) C.P. = Rs 55 and S.P. = Rs 72.60

(ii) C.P. = Rs 490 and S.P. = Rs 416.50

(iii) C.P. = Rs 112, overheads = Rs 14 and S.P. = Rs 94.50

2. Find S.P. when:

(i) C.P. = Rs 435 and loss = 16%

(ii) C.P. = Rs 172, overheads = Rs 61 and gain = 12%

3. A man sells an article at a profit of 25%. If he had bought it at 20% less ad sold it for Rs 10.50 less,

he would have gained 30%. Find the cost price of the article?

4. 20% more can be gained if a piece of cloth is sold for Rs 83 instead of Rs 78. Find the cost price of

the piece of cloth?

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