Percentage quantity aptitude

Percentage

Percent means many hundredths.Example: z% is z percent which means z hundredths. It will be written as:

z% = ^z⁄₁₀₀

^p⁄_q as percent: (^p⁄_q x 100)%

Commodity

If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:[^R⁄_{(100 + R)}x 100]%

If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:[^R⁄_{(100 – R)}x 100]%

Population

The population of a city is P and let it increases at the rate of R% per annum:

Population after t years: P(1 + ^R⁄₁₀₀)^t

• If P is R% more than Q, then Q is less than P by how many percent?
  [^R⁄_{(100 + R)}x 100]%
• If P is R% more than Q, then Q is more than P by how many percent?
  [^R⁄_{(100 – R)}x 100]%

Population t years ago: ^P⁄_{(1 + ^R⁄100)^t}

Depreciation

Let V be the present value of machine. Suppose it depreciates at the rate of R% per annum:

Machine’s value after t years:P(1 – ^R⁄₁₀₀)^t

Machine’s value t years ago: ^P⁄_{(1 – ^R⁄100)^t}