Question

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

• A. They had $36$ and $9$ marbles
• B. They had $30$ and $15$ marbles
• C. They had $41$ and $4$ marbles
• D. They had $20$ and $25$ marbles

Answer 1

Answer: (A)

They had $36$ and $9$ marbles

Let $x$ be the number of marbles john had at the start.
Therefore jivanti had $(45-x)$ marbles.
Now after losing $5$ marbles, each they will have
$(x-5)$ and $(40-x)$ marbles each.
Taking the product we get
$(x-5)(x-40)=-124$
$x^2-45x+200+124=0$
$x^2-45x+324=0$
$(x-36)(x-9)=0$
$x=36$ and $x=9$
Hence, if one has $36$ marbles then the other has $9$ marbles only.