Indian Institute of Foreign Trade 2011 Solved Paper

Let 'x' and 'y' be the average price of 13 books obtained from MN Distributors and remaining 2 books purchased from UV Publishers respectively.
It is given that he spent a total of Rs. 4500. Therefore,
$13\mathit{x}+2\mathit{y}=4500.$......(1)
It is also observed that one-sixth of the average price of all the 15 books purchased is equal to one-fifth of the average price of the 13 books obtained from MN Distributors.
$\frac{4500/15}{6}=\frac{2}{5}$
$\mathit{x}=25$...(2)
Form equation (1) and (2) we can say that $2\mathit{y}=1250.$
Let 'a' and 'b' be the price of two books purchased from UV Publishers. It is given that one-third of the price of one volume is equal to one-half of the price of the other.
Therefore $\frac{\mathit{a}}{3}-\frac{\mathit{b}}{2}$...(3)
Also $2\mathit{y}=1250=\mathit{a}+\mathit{b}$....(4)
From, equation (3) and (4) we can say that $\mathit{a}=750$ and $\mathit{b}=500$.
Hence, option C is the correct answer.