The sum of two numbers is 45. Sum of their quotient and reciprocal is 2.05, Find the product of the numbers.  Choices:
A) 339	B) 500	C) 288	D) 277	E) 112

Rationale: sol : let a , b be the numbers . a + b = 45 ab + baab + ba = 2.05 ⇒ a 2 + b 2 ab ⇒ a 2 + b 2 ab = 2.05 ⇒ ( a + b ) 2 − 2 abab = 2.05 ⇒ ( a + b ) 2 − 2 abab = 2.05 ⇒ ( a + b ) 2 ⇒ ( a + b ) 2 = 2.05 ab + 2 ab = 4.05 ab ⇒ ⇒ ab = 4524 . 054524.05 = 500 answer : b
Answer: B