if \(\frac{m}{n} = \frac{9}{7}\) , then find the cube of \(\frac{{m

if \(\frac{m}{n} = \frac{9}{7}\) , then find the cube of \(\frac{{m - n}}{n}\) up to two places of decimal-

A 22.2

B 0.02

C 1.93

D 10.02

E None of these

Correct Answer: Option B

If (a/b) = (c/d), then,

Componendo-

→ (a+b)/b = (c+d)/d

Divinendo-

→ (a-b)/b = (c-d)/d

Now, given that m/n = 9/7, then according to the rule-

⇒ (m-n)/n = (9-7)/7

= 2/7

Now, cube of 2/7

= (2 × 2 × 2)/(7 × 7 × 7)

= 8/343 = 0.02

Hence, the required answer is 0.02.