Question: The difference of the present ages of two sisters is 5 years. If the product of their ages is 204, find the age of two sisters.

Solution:

Let the present ages of one sister be x years and that of the other be y years.

According to the question,

Condition I,
The difference of their present ages is 5 years.
or, x - y = 5 - (i)

Condition II,
Product of their ages is 204.
or, xy = 204
or, x = \frac{204}{y} - (ii)

Put value of x from equation (ii) in equation (i), we get,

or, \dfrac{204}{y} - y = 5

or, \dfrac{204 - y²}{y} = 5

or, 204 - y² = 5y

or, y² +5y -204 = 0

or, y² + (17-12)y -204 = 0

or, y² + 17y -12y -204 = 0

or, y(y +17) -12(y +17) = 0

or, (y -12)(y +17) = 0

Either,
y -12 = 0
\therefore y = 12

Or,
y +17 = 0
\therefore y = -17

Since, age in years can never be negative, put value of y = 12 in equation (ii), we get,
x = \frac{204}{12}
\therefore x = 17

So, (x,y) = (17,12)

Therefore, the required present ages of two sisters in years are 17 years and 12 years, respectively.

#SciPiPupil