## Saturday, 22 October 2011

### Arithmetic-6 (Profit & Loss)(SNAP2008)

A merchant wants to make profit by selling food grains. Which of the following would maximize his profit?
I.  Sell product at 30% profit
II. Increase the price by 15% over the cost price and reduce weight by 15%
III. Use 700gm of weight instead of 1 kg
IV. Mix 30% impurities in grains and sell it at cost price
(A) III
(B)  II and I
(C)  II
(D) All give same profit
Solution follows here:
Solution:
Assume cost price to be Rs 100 and weight to be 100gm
Option I :
Profit is given as 30%        => Profit ratio= 30/100
Option II :
Increase price by 15% implies new cost price = 115
Reduce weight by 15% implies new weight = 85
So he sells Rs 85 worth of item for Rs 115
Profit ratio= profit/cost = (115-85)/85 = 30/85
Option III :
Using 700gm weight instead of 1kg
So he sells 700 worth of item for 1000
Profit ratio= profit/cost = (1000-700)/700 = 300/700 = 30/70
Option IV :  Mix 30% impurities
If 30% impurities are mixed to a weight of 100, net weight becomes 130. At the presumed rate, he sells this at 130, which means he is selling actual weight of 100gm for Rs 130.
Profit ratio= profit/cost = (130-100)/100 = 30/100
Now compare profit ratios of all the four options respectively:
30/100          30/85                        30/70                        30/100
Numerators are same hence value with lowest denominator is greatest.
Hence option III yields highest profit. Answer (A)