Question 94

The ratio of ages of father and son is 7:2. Five years ago the product of their ages was 150. What is the age of the father?

Solution

Let father's age = $$7x$$ years and son's age = $$2x$$ years

According to ques, => $$(7x-5)(2x-5)=150$$

=> $$14x^2-35x-10x+25-150=0$$

=> $$14x^2-45x-125=0$$

=> $$14x^2-70x+25x-125=0$$

=> $$14x(x-5)+25(x-5)=0$$

=> $$(x-5)(14x+25)=0$$

=> $$x=5,\frac{-25}{14}$$

Since, age can't be negative, thus $$x=5$$

$$\therefore$$ Father's age = $$7 \times 5=35$$ years

=> Ans - (C)

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