The sum of two numbers is 45. Sum of their quotient and reciprocal is 2.05, Find the product of the numbers.  Choose the correct choice from the following answers
A) 339	B) 500	C) 288	D) 277	E) 112
Sol: Let a, b be the numbers.   a + b = 45   ab+baab+ba = 2.05   ⇒a2+b2ab⇒a2+b2ab = 2.05   ⇒(a+b)2−2abab=2.05⇒(a+b)2−2abab=2.05   ⇒(a+b)2⇒(a+b)2 = 2.05ab + 2ab = 4.05ab   ⇒⇒ ab = 4524.054524.05 = 500   Answer:500
<result>B</result>
The sum of two numbers is 45. Sum of their quotient and reciprocal is 2.05, Find the product of the numbers.