Finding the magnitude and direction of current thro Kirchhoff law

[logearav]

Homework Statement

Revered Members,
Please go through my attachment. I have been asked to find the magnitude and direction of current through the 10 ohm resistor. The answer that is given in the book is 1/23 Ampere from A to B.
But i solved as given in the attachment but i got the answer as 5/37 Ampere which is I₃...the current which I assumed to pass through 10 ohm resistor. Since Please help me where i went wrong.

Homework Equations

The Attempt at a Solution

 

[gneill]

Your work and results look fine. Must be an error in the book's answer.

 

[rude man]

I used the superposition principle as follows:

1. Short the 2V source & get voltage across the 10Ω = +2.1622V.
2. Short the 8V source and get same voltage = -0.8108V
3. Superpose the voltages to get +1.3514V across the 10Ω.
4. Divide by 10Ω to get i3 = 0.13514A which agrees with both of you!

 

[logearav]

Thank you gneill and rude man for your help.