## Question

Please help in the solution the following problem In what proportion must water be mixed with milk so as to gain 20% by selling the mixture at the cost price of the milk ? How to solve this kind problem , is there any general method/formula .

## general method/formula .

suppose the original quantity is x units and rate is Rs 1/unit the C.P. = x.1 = Rs x suppose it is adulterated with y % of fake item new quantity is x+(y% of x) the S.P. is also 1 the cash inflow = [x+(y% of x)].1 profit = [x+(y% of x)] minus x = y% of x percentage profit = (y% of x)/x = y % i.e. if profit required is y% adulteration required is y% if profit required is 20% adulteration required is 20 %(i.e. 1/5)