## Profit, Loss and Interest

Theory

Profit, Loss and Discount as well as Simple and Compound Interest are two of the easiest topics in quantitative section. Every year, a small number of questions appear from each of these sections and good students should aim to get all the questions right from these topics. The number of concepts in these topics is limited and most of the problems can be solved by applying the formulae directly. Many students commit silly mistakes in this topic due to complacency and this should be avoided.

Formula

The cost price of an article is C.P, the selling price is S.P and the marked price is M.P

• Profit (Loss) = S.P – C.P
• % Profit (Loss) = Profit (Loss)/C.P *100
• Discount = M.P – S.P
• % Discount = Discount/M.P * 100
• Total increase in price due to two subsequent increases of X% and Y% is (X+Y+XY/100)%
Formula

The principal amount is P, rate of interest is R and time of loan is T

• Simple Interest = $$\frac{P*T*R}{100}$$
• Amount = Principal + Simple Interest
• Compound Interest = $$P(1+\frac{R}{100})^{T}$$ - P
• For the same principal, positive rate of interest and time period, the compound interest on the loan is always greater than the simple interest.
Formula

When there are two successive profits of $$x\%$$ and $$y\%$$ then the net percentage profit $$=\ \frac{\ x+y+xy}{100}$$.

When there is a profit of $$x\%$$ and loss of $$y\%$$ then net percentage profit or loss $$=\ \frac{\ x-y-xy}{100}$$

Formula

A dishonest dealer claims to sell his goods at cost price, but he uses a weight of lesser weight, then the gain% = $$=\ \ \frac{\ true\ weight\ -\ false\ weight}{false\ weight}\times\ 100\%$$

A dishonest dealer sells an item at a profit of x % and uses a weight that is y % less, then the gain%  $$=\ \ \frac{\ \%\ profit\ +\ \%\ less\ in\ weight}{100-\ \%\ less\ in\ weight}\times\ 100\%$$

Formula

If an amount 'P' is borrowed for 'n' years at r% per annum compounded annually, and x is the installment that is paid at the end of each year, starting from the first year, then:

$$P\ =\ \frac{\ x}{1+\frac{r}{100}}+\ \frac{\ x}{\left(1+\frac{r}{100}\right)^{^2}}+...+\ \frac{\ x}{\left(1+\frac{r}{100}\right)^{^n}}$$