Percentage

Percentage - Shortcut tricks formula

1. If P is m% more than Q, then Q is less than P by $$ =\frac{m}{(100 + m)} \times 100$$
2. If P is m% less than Q, then Q is more than P by $$ =\frac{m}{(100 - m)} \times 100$$
3. If there is m% increase in the price of an article, then its sales fall by n%, then the percentage of increase or decrease in the income of a shopkeeper $$=(m - n) - \frac{m \times n}{100}$$
4. In the above statement, when there is a decrease of m% and an increase of n%, then the percentage of decrease or increase in the income $$=(- m + n) - \frac{m \times n}{100}$$ Note : - A positive (+) value indicates a percentage increases and a negative (-) value indicates percentage decreases.
5. When there is a m% increases in the price of commodity, by what percentage should a person reduce its consumption so that his expenditure remains the same $$ =\frac{m}{(100 + m)} \times 100$$
6. When there is a m% decreases in the price of commodity, by what percentage should a person increase its consumption so that his expenditure remains the same $$ =\frac{m}{(100 - m)} \times 100$$
7. Let the population of a town be A, now and suppose it increases at the rate of R% per annum, then : $$1. \; Population \;after\; t\; years = A\left[1 + \frac{R}{100}\right]^t$$ $$2.\; Population\;before\; t\; years =\frac{A}{1+\left[\frac{R}{100}\right]^t}$$
8. If a person saves Rs. X by spending m% of his income on food, n% on clothes and p% on entertainment, then his monthly income is $$ = \frac{100}{100 - (m + n + p)} \times X$$