The ratio of two numbers a and b is 7: 15, respectively. Their least common multiple is 84. What is (b+a):(b-a) ?

Correct option is B

Given:
Ratio of Numbers = 7 : 15
LCM = 84
Concept Used:
If 'a' and 'b' are two numbers, then LCM × HCF = a × b
Solution:
Let the numbers 'a' and 'b' be 7x and 15x.
LCM × HCF = a × b
=> 84 × x = 7x × 15x
=> x = $$\frac {4}{5}$$​
​$$a = 7x \\\Rightarrow a = 7 \times \frac{4}{5} \\\Rightarrow a = \frac{28}{5} \\[10pt]b = 15x \\\Rightarrow b = 15 \times \frac{4}{5} \\\Rightarrow b = 12 \\[10pt](b + a) : (b - a) = \left(12 + \frac{28}{5}\right) : \left(12 - \frac{28}{5}\right) \\\Rightarrow \frac{60 + 28}{5} : \frac{60 - 28}{5} \\\Rightarrow \frac{88}{5} : \frac{32}{5} \\\Rightarrow 88 : 32 \\\Rightarrow 11 : 4 \\[10pt]\therefore (b + a) : (b - a) = 11 : 4$$​​