Question

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.​

Answer 1

$\blue{\huge{\underline{\underline{Solution:-}}}}$

Given Rahul and Rohan 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

Answer 2

Step-by-step explanation:

\blue{\huge{\underline{\underline{Solution:-}}}}Solution:−

Given Rahul and Rohan 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