Question 94

The sum of the ages of brother and sister at present is 21. Five years ago the product of their ages was 28. What is the age of the brother and the sister?

Solution

Let the age of brother = $$x$$ years and sister's age = $$(21-x)$$ years

Product of their ages 5 years ago = $$(x-5)(21-x-5) = 28$$

=> $$(x-5)(16-x)=28$$

=> $$16x-x^2-80+5x=28$$

=> $$x^2-21x+108=0$$

=> $$x^2-9x-12x+108=0$$

=> $$x(x-9)-12(x-9)=0$$

=> $$(x-12)(x-9)=0$$

=> $$x=12,9$$

$$\therefore$$ Ages of brother and sister are 12 and 9

=> Ans - (A)

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