Question

q1.Rahul and Rohan have 45 marbles together. After losing 5 marbles each, the product of the number of marbles they both have now is 124. How to find out how many marbles they had to start with.
This is from chapter Quadratic Equation Class 10

Answer 1

Given John and Jivanti together have 45 marbles

Let the number of Marbles Rahul had be =x

Then the number of marbles Rohan had=45−x

Both of them lost 5 Marbles each

Therefore, the number of marbles Rahul had=x−5

The number of marbles Rohan had=45−x−5=40−x

Now product of the number of Marbles =124

∴(x−5)(40−x)=124

40x−x²−200+5x=124

−x²+45x−200−124=0

x²−45x+328=0 --- (Multiplying by(-1))

By factorization method

x2−36x−9x+324=0

x(x−36)−9(x−36)=0

(x−36)(x−9)=0

x=36 or x=9

When Rahul has 36 Marbles, Rohan has =45−x=45−36=9 marbles

When Rahul has 9 Marbles and Rohan has =45−x=45−9=36 marbles

Hope this helps you!

=)