# Percentage Shortcut Methods

Percent is derived from a phrase in latin “per centum” which means per hundred. It is a ratio with base (denominator) 100. It evolved as a concept so that there can be a uniform platform for comparing different values.

To express x% as a fraction, divide it by 100 ⇒ x% = x/100

To express a fraction as %, multiply it by 100 ⇒ x/y = [(x/y) × 100] %

x% of y is given by (y × x/100 )

1/4 = 25%

1/5 = 20%

1 /6= 16.66%

1/7 = 14.28%

1/8 = 12.5%

1/9 = 11.11%

1/10 = 10%

1/11 = 9.09%

1/12 = 8.33%

Shortcuts

If X’s income is a% more than Y’s income, the Y’s income is less than X’s income by

[ a / (100+a)] * 100%

If ‘M’ is x% of ‘N’ and ‘P’ is y% of ‘N’ then

‘M’ is (x/y) * 100% of ‘P’.

If the sides of the triangle, rectangle, square, circle, rhombus etc is

(i) Increased by a%. Its area is increased by

2a+(a2/100)

(ii)If decreased b%. Its areas is decreased by,

-2b+(b2/100)

The population of a town is ‘P’. It increased by x% during 1st year, increased by y% during 2nd year and again increased by z% during 3rd year. The population after 3 years will be,

P *[(100+x)/100] * [(100+y)/100] * [(100+z)/100]

(193)