Question

The sum of ages of Eera and her sister is 46 and the product of their ages is 465. What are their ages?

(a) Eera 31, Her sister 15

(b) Eera 5, Her sister 10

(c) Eera 12, Her sister 37

(d) Eera 57, Her sister 12

This question was posed to me in semester exam.

I'm obligated to ask this question of Solution of Quadratic Equation by Squaring Method topic in division Quadratic Equation of Mathematics – Class 10

Answer 1

Right option is (a) Eera 31, Her sister 15

The explanation: Let the age of Eera be x years. The age of her sister will be 46-x years.

The product of their ages is 465.

x(46-x)=465

46x-x^2=465

x^2-46x+465=0

x^2-46x=-465

Adding \(\frac {b^2}{4}\) on both sides, where b=-46

x^2 – 46x + \(\frac {-46^2}{4}=\frac {-46^2}{4}\) – 465

x^2 – 46x + \(\frac {2116}{4}=\frac {2116}{4}\) – 465

x^2 – 46x + \(\frac {2116}{4}=\frac {256}{4}\)

\((x-\frac {46}{2})\)^2=\((\frac {16}{2})\)^2

x-\(\frac {46}{2}\)=±\(\frac {16}{2}\)

x = \(\frac {16}{2}+\frac {46}{2}=\frac {62}{3}\) = 31 and x = \(\frac {-16}{2}+\frac {46}{2}=\frac {30}{2}\) = 15

The ages of Eera and her sister are 31 and 15 respectively or 15 and 31 years.