efficiency of the heat engine is calculated by the formula
![\eta = 1- (T_c)/(T_h)](https://img.qammunity.org/2019/formulas/physics/middle-school/kl726v0yc9pd2s4oooov6rgijga8ekkdyt.png)
here we know that
= cold temperature
= hot temperature
now we will find the efficiency of all
1) for W
![\eta_1 = 1- (T_c)/(T_h)](https://img.qammunity.org/2019/formulas/physics/middle-school/yxla4seh3z0hzqsxpcgxcs5xhofnff6e4x.png)
![\eta_1 = 1- (120)/(620)](https://img.qammunity.org/2019/formulas/physics/middle-school/doskwz0we4u948dlzr0by21sff1f400nzm.png)
![\eta_1 = 0.806](https://img.qammunity.org/2019/formulas/physics/middle-school/hq4aud316v1j5uuaazfdpi2n9ssn85cusn.png)
2) for X
![\eta_2 = 1- (T_c)/(T_h)](https://img.qammunity.org/2019/formulas/physics/middle-school/ypfqru3t06rngxjngw2d3eivn3ctw1r4v9.png)
![\eta_2 = 1- (100)/(840)](https://img.qammunity.org/2019/formulas/physics/middle-school/sbypp3fbv1u1ica5l1086qx7urnnxyfhyg.png)
![\eta_2 = 0.88](https://img.qammunity.org/2019/formulas/physics/middle-school/ay4azkmhjt0gh9a1kxh8pqij969gmq3igi.png)
3) For Y
![\eta_3 = 1- (T_c)/(T_h)](https://img.qammunity.org/2019/formulas/physics/middle-school/az5iz5pd7jx441yvpxwqv7ut65svkv9i0c.png)
![\eta_3 = 1- (300)/(900)](https://img.qammunity.org/2019/formulas/physics/middle-school/xukg4r7ht7cmhn29088a8whnhg2xgmxfdj.png)
![\eta_2 = 0.67](https://img.qammunity.org/2019/formulas/physics/middle-school/rmytmfrlfiacnbbdeypgm5rob43t6y5kk8.png)
4) for Z
![\eta_4 = 1- (T_c)/(T_h)](https://img.qammunity.org/2019/formulas/physics/middle-school/7daqk51clfn1il7r9gbrucds2htip5sba4.png)
![\eta_4 = 1- (25)/(500)](https://img.qammunity.org/2019/formulas/physics/middle-school/h6h41sop312dtvbst7dygghgneljslaivj.png)
![\eta_4 = 0.95](https://img.qammunity.org/2019/formulas/physics/middle-school/1mfkwexszbfv18t5bkyjitfny9t7r6n44c.png)
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