Question

The sum of two digit number is 16 and the sum of their reciprocal is 1/3 . Find the numbers

Answer 1

Let the two numbers be x and y
Therefore x +y =16....(1)
Again
1/x +1/y =1/3
x+y/xy = 1/3 ⇒ xy=3*16
⇒ xy =48
⇒x = 48/y
On putting value of x in eq(1) we get
48/y +y =16
⇒48 + y² = 16 y
⇒y²- 16y + 48 = 0
⇒y²- 12y - 4y +48 =0
⇒ (y - 12) (y - 4) = 0
⇒ y = 12 or 4
Now for y = 12 ,x =16 - 12 =4
and for y = 4 ,x =16 - 4 = 12
 so 12 and 4 are the answers.

Answer 2

Answer:

Step-by-step explanation: