Question 68
Two numbers are such that their product, their sum and their difference are in the ratio 24 : 7 : 1. Then their product is
Solution
Let the numbers be $$a$$ and $$b$$
According to ques, => $$ab:(a+b):(a-b)=24:7:1$$
Thus, $$\frac{a+b}{a-b}=\frac{7}{1}$$
=> $$a+b=7a-7b$$
=> $$6a=8b$$
=> $$\frac{a}{b}=\frac{4}{3}$$
Let $$a=4y$$ and $$b=3y$$
Also, $$\frac{ab}{a-b}=\frac{24}{1}$$
=> $$\frac{4y\times3y}{4y-3y}=24$$
=> $$12y^2=24y$$
=> $$y=2$$
$$\therefore$$ Numbers are $$a=8$$ and $$b=6$$
=> Product = $$ab=8\times6=48$$
=> Ans - (B))
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