If A can buy 15 books less for Rs.900 when the price of each book goes

Explanation
Since the number of books is not given, I could not plug in the values. So this is solved using quadratic equations.
This is how i solved.
Let the number of books bought initially for Rs.900 be 'x'. So the original price of the book was 900/x
Now price of the book is up by 3. i.e., (900/X) + 3. and number of books bought is reduced by 15. i.e., (x-15)
Since new total amount spent is still same, the product of new price and new number of books is still 900

[(900/x)+3] (x-15) = 900
(900+3x) (x-15) = 900x
3x^2 +855-13500 = 900x Now use quadratic equation to find the value of x.
x^2 -15x-4500 = 0
x^2 -75x+60x-4500 =0
x(x-75)+60(x-75) =0
(x-75) (x+60) =0
so x = 75 or x = 60
since x cannnot be negative, x = 60
Thus the original price of the book = 900/75 = 12
Answer B.

Using the options was pretty much what I thought of too.
One look at 14 and 16 and you know they cannot be the answers since number of books bought must be an integer but 900/14 and 900/16 will not be integers. (Don't divide to check this. 900 is not divisible by 7 and 900 is divisible only by 4, not 16)

If 10 was the original price, then number of books must have been 90.
Reducing by 15, 75 books, each at Rs. 13 will not make Rs. 900 since the product will not end with a 0.

12 is the only possible answer. Confirm it. 900/12 = 75
Reducing by 15, 60 books, each at Rs. 15 will make Rs. 900.

if you quickly notice the revised price(after adding 3 to original) of 15 only divides 900. So 12 is the answer

backward solving is more suitable here

If A can buy 15 books less for Rs.900 when the price of each book goes up by Rs.3. find the original initial price.

Let N and P be the no. of books and the price of each book before the raise
According to given scenario,

=>NP=(N-15)(P+3)=900
=>NP+3N-15P-45=900
=>3N-15P-45=0
Substituting N=900/P
=>2700-15P^2-45P=0
=>P^2+3P-180=0

Using the options, we get P=12

Hence B