Two numbers are such that their difference, their sum and their produc

1.	Two numbers are such that their difference, their sum and their product are to one another is 1 : 7 : 24. The product of two numbers is A) 12 B) 24 C) 48 D) 96
Answer» Correct option is (C) 48 Let both numbers are a & b. \(\therefore\) Their sum = a+b, their difference = a - b and their product = ab According to given condition, a - b : a+b : ab = 1 : 7 : 24 \(\Rightarrow\frac{a-b}{ab}=\frac1{24}\) and \(\frac{a+b}{ab}=\frac7{24}\) \(\Rightarrow\) \(\frac1b-\frac1a=\frac1{24}\) and \(\frac1b+\frac1a=\frac7{24}\) \(\Rightarrow\) \((\frac1b-\frac1a)+(\frac1b+\frac1a)=\frac1{24}+\frac7{24}\) \(\Rightarrow\) \(\frac2b=\frac8{24}=\frac1{3}\) \(\Rightarrow\) \(b=2\times3=6\) \(\therefore\) \(\frac16-\frac1a=\frac1{24}\) \(\Rightarrow\) \(\frac1a=\frac16-\frac1{24}\) \(=\frac{4-1}{24}=\frac{3}{24}=\frac{1}{8}\) \(\Rightarrow\) a = 8 \(\therefore\) Product of both numbers = ab \(=8\times6=48\) Correct option is B) 24

Two numbers are such that their difference, their sum and their product are to one another is 1 : 7 : 24. The product of two numbers is A) 12 B) 24 C) 48 D) 96

Answer»

Correct option is (C) 48

Let both numbers are a & b.

\(\therefore\) Their sum = a+b,

their difference = a - b and

their product = ab

According to given condition,

a - b : a+b : ab = 1 : 7 : 24

\(\Rightarrow\frac{a-b}{ab}=\frac1{24}\) and \(\frac{a+b}{ab}=\frac7{24}\)

\(\Rightarrow\) \(\frac1b-\frac1a=\frac1{24}\) and \(\frac1b+\frac1a=\frac7{24}\)

\(\Rightarrow\) \((\frac1b-\frac1a)+(\frac1b+\frac1a)=\frac1{24}+\frac7{24}\)

\(\Rightarrow\) \(\frac2b=\frac8{24}=\frac1{3}\)

\(\Rightarrow\) \(b=2\times3=6\)

\(\therefore\) \(\frac16-\frac1a=\frac1{24}\)

\(\Rightarrow\) \(\frac1a=\frac16-\frac1{24}\)

\(=\frac{4-1}{24}=\frac{3}{24}=\frac{1}{8}\)

\(\Rightarrow\) a = 8

\(\therefore\) Product of both numbers = ab

\(=8\times6=48\)

Correct option is B) 24