Given: The age of 3 sisters are in constant proportion. Age of second sister is 12 years. Difference between first and third sister is 7 years. Concept Used: Constant proportion, ⇒ a/b = b/c Calculation: Let the age of 3 sisters be a, b and c respectively. ⇒ b = 12 years and a – c = 7 years a/b = b/c ⇒ b2 = a × c Putting the value of b, ⇒ 122 = a × c ⇒ 144 = a × c We have a – c = 7 and a × c = 144. ⇒ a = 7 + c ⇒ (7 + c)c = 144 ⇒ 7c + c2 – 144 = 0 ⇒ c2 + 7c – 144 = 0 ⇒ c2 + 16c – 9c – 144 = 0 ⇒ c (c + 16) – 9 (c + 16) = 0 ⇒ c – 9 = 0 or c + 16 = 0 ⇒ c = 9 or –16 Age cannot be negative. The age of c is 9 years. a = 7 + c ⇒ a = 7 + 9 ⇒ a = 16 years. ∴ The age of first sister is 16 years.