**Aptitude & Reasoning**

RATIO- PERCENTAGE – ALLEGATIONS & MIXTURES

If the price of commodity increases by X%, then the reduction in the consumption

so as not to increase the expenditure = ( x / 100 + x )× 100

And, in case of decrease = (x/100 − x) × 100

Let the population of a city be ‘P’ now and suppose it increases at the rate of R%

per annum, then

Population after n- years = p × (1 + R/100)^n

Population n- years ago = P/ (1+R/100)^n

If A is R% more than B, then B is less than A by = (R / 100 + R)∗ 100

If A is R% less than B, then B is more than A by = (R/100 − R) ∗ 100

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