The cost of raw materials of a product increases by 30%, the manufacturing cost increases by 20% and the selling price of the product increases by 60%. The raw material and the manufacturing cost originally formed 40% and 60% of the total cost respectively. If the original profit percentage was one - fourth the original manufacturing cost, find the approximate new profit percentage.

Explanation:-

Let the total initial cost of production be Rs. 100
Then,
manufacturing cost = Rs. 60.
Cost of raw materials = Rs. 40.
Original Selling Price $$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {100 + \frac{{60}}{4}} \right) \cr & = {\text{Rs}}{\text{. }}115 \cr}$$ New cost of raw materials = 130% of Rs. 40 = Rs. 52
New Manufacturing cost = 120% of Rs. 60 = Rs. 72
New cost of the product = Rs. (52 + 72) = Rs. 124
New S.P. = 160% of Rs. 115 $$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {\frac{{160}}{{100}} \times 115} \right) \cr & = {\text{Rs}}{\text{. }}184 \cr}$$ New profit = Rs. (184 - 124) = Rs. 60 $$\eqalign{ & \therefore {\text{New profit }}\% \cr & = \left( {\frac{{60}}{{124}} \times 100} \right)\% \cr & = 48.39\% . \cr}$$