Question 83

The brother is elder to his sister by 6 years. Seven years ago the product of their ages was 72. What is the age of the brother?

Solution

Let age of brother = $$x$$ years

=> Age of sister = $$(x - 6)$$ years

Product of their ages 7 years ago = $$(x - 7) \times (x - 13) = 72$$

=> $$x^2 - 13x - 7x + 91 - 72 = 0$$

=> $$x^2 - 20x + 19 = 0$$

=> $$x^2 - x - 19x + 19 = 0$$

=> $$x(x - 1) - 19(x - 1) = 0$$

=> $$(x - 1) (x - 19) = 0$$

=> $$x = 1 , 19$$

Since, $$x \neq 1$$, => Age of brother = 19 years

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