Correct Answer - Option 3 : 80%
Concept:
Indicated power = Brake power + Frictional power
Let Brake power per cycle = B,
Indicated Power per cycle = I,
Friction Loss per cycle = F
Then,
When all the cylinders are working then
4I = 4B + 4F
When one cylinder is cut one by one, 4 different reading is taken for 3 working cylinders then the average value will be
\(3{\rm{B\;}} = {\rm{\;}}\frac{{3{{\rm{B}}_1} + {\rm{\;}}3{{\rm{B}}_2}{\rm{\;}} + {\rm{\;}}3{{\rm{B}}_3}{\rm{\;}} + {\rm{\;}}3{{\rm{B}}_4}{\rm{\;}}}}{4}\)
For three working cylinders
3I = 3B + 4F
For four working cylinders
4I = 4B + 4F
From two equations of I
I = 4B – 3B
4I = 4 × (4B – 3B)
Calculation:
Given that, 4B = 80 kW, B1 = 55 kW, B2 = 55.5 kW, B3 = 54.5 kW and B4 = 55 kW
Then \(3{\rm{B\;}} = {\rm{\;}}\frac{{55 + 55.5{\rm{\;}} + {\rm{\;}}54.5{\rm{\;}} + {\rm{\;}}55{\rm{\;}}}}{4} = 55\;kW\)
I = 4B – 3B = 80 – 55 = 25 kW
4I = 25 × 4 = 100 kW
\({\eta _m} = \frac{{Net\;B.P}}{{Net\;I.P}} = \frac{{80}}{{100}} = 80\% \)