Hello There!!
We are given to find efficiency of the cycle.
We Know
Efficiency is denoted by the symbol "η"
[tex] \text{η\%} = \frac{ \text{Output Work}}{ \text{Heat Supplied } } \times 100[/tex]
As it is a cyclic process, So,
[tex] \triangle \text{U} = 0 \\ \implies \triangle \text{ Q} = \triangle \text{W} + \triangle \text {U} \\ \implies\triangle \text{ Q} = \triangle \text{W} + 0 \\ \implies \triangle \text{Q} = \triangle \text{W}[/tex]
[tex] \text{Let us first calculate} \: \triangle \text{Q}[/tex]
[tex]\triangle \text{Q} = \text{Q}_1 + \text{Q}_2 + \text{Q}_3 + \text{Q}_4[/tex]
[tex]\triangle \text{Q} = 1000 + ( - 800) + 450 + (- 200) \\ \\ \implies\triangle \text{Q} = 1000 - 800 + 450 - 200 \\ \\ \implies \triangle \text{Q} = 450 \text{J}[/tex]
[tex]\therefore \text{ Net Output Work i.e., ∆W = 450 J}[/tex]
Now, We need to find the Heat Input.
We know, Heat Input is always the sum of all positive heats
[tex] \because {∆Q_{in}} = \text{∆Q}_1 + \text{∆Q}_3 \\ \\ 1000 + 450 = 1450 \text{J}[/tex]
Now We Have To Find The η%
[tex] \text{η\%} = \frac{ \text{Output Work}}{ \text{Heat Supplied } } \times 100[/tex]
[tex] \text{η\%} = \frac{ \text{450}}{ \text{1450 } } \times 100 \\ \\ \implies \text{η\%} = \frac{ \text{450}}{ \text{145} \cancel{0 } } \times 10 \cancel0 \\ \\ \implies\text{η\%} = \frac{ \text{450}}{ \text{145 } } \times 10 \\ \\ \implies{ \text{η\%}} = \frac { \cancel{450}}{ \cancel{145}} \times 10 \: \: \: \: \fbox{cancelling by 5} \\ \\ \implies{ \text{η\%}} = \frac{90}{29} \times 10 \\ \\ \implies{ \text{η\%}} = 31.0344\% \\ \\ \implies{ \text{η\%}} = \red{31\%}[/tex]
Option A= 31% is the correct answer
Hope this helps!!
