For any two numbers m , n ; (m+n) : (m-n) : mn = 7: 1: 60 . Find the value of 1/m : 1/n

Q: For any two numbers m , n ; (m+n) : (m-n) : mn = 7: 1: 60 . Find the value of 1/m : 1/n

m + n m - n = 7 x x ⇒ m n = 4 x 3 x Again m n = 12 x 2 and mn =60x so, 60 x = 12 x 2 ⇒ x = 5 => m= 20 and n= 15 Hence, 1 m : 1 n = 1 20 : 1 15 = 3 : 4

4:3
8:7
3:4
7:8

Correct Answer: 3:4

Explanation:

$\frac{m + n}{m - n} = \frac{7 x}{x} \Rightarrow \frac{m}{n} = \frac{4 x}{3 x}$

Again $m n = 12 x 2$

and mn =60x

so, $60 x = 12 x 2 \Rightarrow x = 5$

=> m= 20 and n= 15

Hence, $\frac{1}{m} : \frac{1}{n} = \frac{1}{20} : \frac{1}{15} = 3 : 4$

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