n Punjab, any person consuming energy has to pay a fixed charge and an additional amount proportional to the energy (in kilowatt (kwh)) consumed and if a person consumes more than 60 kwh per month, one has to pay an amount proportional to the square root of energy consumed (in kwh) in addition to the first additional amount. If a person pays ₹400 for 50 kwh, ₹360 for 30 kwh and ₹498 for 81 kwh, how much should he pay for 100 kwh (in ₹)?

The problem can be solved by setting up a system of linear equations. Let's denote the fixed charge as F, the additional amount proportional to the energy consumed as A, and the amount proportional to the square root of energy consumed as B.

From the problem, we have the following equations:

1. F + 50A = 400 (for 50 kwh)
2. F + 30A = 360 (for 30 kwh)
3. F + 60A + B*sqrt(81) = 498 (for 81 kwh)

Subtracting the second equation from the first gives us 20A = 40, so A = 2.

Substituting A = 2 into the first equation gives us F + 100 = 400, so F = 300.

Substituting A = 2 and F = 300 into the third equation gives us 300 + 120 + 9B = 498, so B = 8.

Therefore, for 100 kwh, the person should pay F + 100A + B*sqrt(100) = 300 + 200 + 80 = ₹580.

The problem can be solved by setting up a system of linear equations.

Let's denote the fixed charge as F, the additional amount proportional to the energy consumed as A, and the amount proportional to the square root of energy consumed as B.

From the problem, we can set up the following equations:

1. F + 50A = 400 (for 50 kwh)
2. F + 30A = 360 (for 30 kwh)
3. F + 81A + B*sqrt(81) = 498 (for 81 kwh)

Subtracting the second equation from the first gives us 20A = 40, so A = 2.

Substituting A = 2 into the first equation gives us F + 100 = 400, so F = 300.

Substituting F = 300 and A = 2 into the third equation gives us 300 + 162 + 9B = 498, so B = 4.

Therefore, for 100 kwh, the person should pay F + 100A + Bsqrt(100) = 300 + 200 + 410 = 500 + 40 = ₹540.