Question 86
The sum of the ages of husband and wife at present is 56. Ten years ago the product of their ages was 320. What is the age of the husband and the wife?
Solution
Let husband's age = $$x$$ years
=> Wife's age = $$(56 - x)$$ years
According to ques, $$(x-10)(56-x-10)=320$$
=> $$(x-10)(46-x)=320$$
=> $$46x-x^2-460+10x=320$$
=> $$x^2-56x+780=0$$
=> $$x^2-30x-26x+780=0$$
=> $$x(x-30)-26(x-30)=0$$
=> $$(x-30)(x-26)=0$$
=> $$x=30,26$$
$$\therefore$$ Ages of the husband and the wife = 30 and 26 years
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