Question

Only a genius can solve.
Carol was given three non negative unequal numbers and was asked to add

the largest of the three to the product of the other two. Instead, she

multiplied the largest with the sum of the other two, but still got the right

answer. What is the sum of the three numbers?​

Answer 1

Answer:

Multiple solution exist

1/2  , 3/4  & 3/2  Sum = 11/4

1/2  , 5/8  & 5/2  Sum = 29/8

Step-by-step explanation:

Three numbers  A B & C

C > B > A

add   the largest of the three to the product of the other two

AB + C

multiplied the largest with the sum of the other two

C(A + B)

AB + C  = C(A + B)

=> AB + C  =  AC  + BC

=> C(1 - A) = B(C - A)

As C > A  => 1 > A

Let take A = 1/2

B/2 + C = C(B + 1/2)

=> B/2 + C = BC + C/2

=> B/2 + C/2 = BC

=> B + C = 2BC

Let take  B = 3/4

Then

3/4 + C = 2(3/4)C

=> 3/4 + C = 3C/2

=> 3/4 = C/2

=> C = 3/2

A = 1/2  , B = 3/4  & C= 3/2

(1/2 * 3/4)  + 3/2 =  3/8 + 3/2 = 15/8

(1/2 + 3/4)*(3/2)  =  (5/4)*(3/2) = 15/8

A + B + C =  1/2 + 3/4  + 3/2  =  11/4  

sum of the three numbers = 11/4

Let take  B = 5/8

Then

5/8 + C = 2(5/8)C

=> 5/8 + C = 5C/4

=> 5/8 = C/4

=> C = 5/2

A = 1/2  , B = 5/8  & C= 5/2

(1/2 * 5/8)  + 5/2 =  5/16 + 5/2 = 45/16

(1/2 + 5/8)*(5/2)  =  (9/8)*(5/2) = 45/16

A + B + C =  1/2 + 5/8  + 5/2  = 29/8  

sum of the three numbers = 29/8