Correct Answer - Option 2 : 11 : 4
Given:
Ratio of Numbers = 7 : 15
LCM = 84
Concept used:
If 'a' and 'b' are two numbers, then LCM × HCF = a × b
Calculations:
Let the numbers 'a' and 'b' be 7x and 15x.
LCM × HCF = a × b
⇒ 84 × x = 7x × 15x
⇒ x = 4/5
a = 7x
⇒ a = 7 × 4/5
⇒ a = 28/5
b = 15x
⇒ b = 15 × 4/5
⇒ b = 12
(b + a) : (b - a) = (12 + 28/5) : (12 - 28/5)
⇒ (60 + 28)/5 : (60 - 28)/5
⇒ 88 : 32
⇒ 11 : 4
∴ (b + a) : (b - a) is 11 : 4.
