efficiency of the heat engine is calculated by the formula
[tex]\eta = 1- \frac{T_c}{T_h}[/tex]
here we know that
[tex]T_c [/tex] = cold temperature
[tex]T_h [/tex] = hot temperature
now we will find the efficiency of all
1) for W
[tex]\eta_1 = 1- \frac{T_c}{T_h}[/tex]
[tex]\eta_1 = 1- \frac{120}{620}[/tex]
[tex]\eta_1 = 0.806[/tex]
2) for X
[tex]\eta_2 = 1- \frac{T_c}{T_h}[/tex]
[tex]\eta_2 = 1- \frac{100}{840}[/tex]
[tex]\eta_2 = 0.88[/tex]
3) For Y
[tex]\eta_3 = 1- \frac{T_c}{T_h}[/tex]
[tex]\eta_3 = 1- \frac{300}{900}[/tex]
[tex]\eta_2 = 0.67[/tex]
4) for Z
[tex]\eta_4 = 1- \frac{T_c}{T_h}[/tex]
[tex]\eta_4 = 1- \frac{25}{500}[/tex]
[tex]\eta_4 = 0.95[/tex]
So here most efficient engine is Z and least is Y
so we can arrange it as
Z > X > W > Y
so 3rd option is correct here