The product of the ages of Shyam and Ram is 240 If double the age of Ram is more than Shyam 39 s age...........

Quantitative Aptitiude (CLAT) Problems based on Ages

The product of the ages of Shyam and Ram is 240. If double the age of Ram is more than Shyam's age by 4 years, what is Ram's present age?

Explanation:

: Let the age of Ram = X years
Age of Shyam = Y years
According to question
XY= 240 ............eq.1
And, 2X = Y + 4
Y= 2X- 4
Y = 2(X-2) ...............eq.2

Now putting the value of eq.2 in eq.1
X ×[ 2(X-2)] = 240
X × (2X - 4) =240
2X² - 4X =240
X²- 2X = 120
X² - 2X - 120 = 0

Doing the factors of above equation:
X² - (12-10)X - 120 = 0
X² -12X + 10X -120 = 0
X(X-12) + 10(X-12) = 0
(X-12) (X+10) = 0
X+10 = 0, X-12 = 0
X= -10, X = 12
Therefore Ram's age is 12 years.