Question

Ravi and Raj together have $45$ marbles. Both of them lost $5$ marbles each, and the product of the number of marbles they now have is $124$. Find out the number of marbles they had to start with.

• A. $36$ and $9$
• B. $40$ and $5$
• C. $20$ and $25$
• D. $14$ and $31$

Answer 1

The correct option is A $36$ and $9$

Let Ravi have x, marbles.
Hence
Raj has $45-x$ marbles.
Now applying the above condition, we get
$(x-5)(45-x-5)=124$
$(x-5)(x-40)=-124$
$x^2-45x+200+124=0$
$x^2-45x+324=0$
$(x-36)(x-9)=0$
Hence
$x=36$ or $x=9$
Thus if one had 9 marbles then the other had 36 marbles.