mesh analysis question with dependent current source

Consider 3 loops 1 st loop::50-25i¹+20i²=0 (I=-i) 2,3 loops::20i¹-20i²-10i²-22.5i³=0 [as there is dependent source between loops these two loop equations will combine] Equation between dependent source::3I=i³-i² substitue I=-i Solve 3 equations we get i¹=-6A,i²=-10A,i³=8A V=i³R V=8×22.5=180V
Hence solved V=180V Note::‼ don't consider those as powers of current consider them like base of powers which I have wrote for ur clarification

Kirchhoff's Voltage Law (KVL) says the the sum of voltages around closed loop is zero. This is the basis for Mesh Analysis.

In your equation for the M1 mesh (which is correct), you have the voltages across the source and two resistors summing to zero. But the equations for M2 and M3 are missing the voltage across the dependent current source. This is why you're not able to get the correct answer.

It's more convenient to work this problem using Nodal Analysis, which is based on KCL. There are only two node voltages to solve for, and expressions for the currents are straightforward.

It appears that Pranabendra beat me to providing a worked answer, but I thought I would explain what is wrong with your original attempt.

Mesh analysis is based on Kirchoff's voltage law, which states that if we consider the voltages around any closed loop in a circuit we have $$ V_1 + V_2 + ldots + V_n = 0$$ so that all the potential differences add to zero. The idea of mesh analysis is that if we can write the voltage across each component as either a constant or a simple function of the current through that component, then KVL allows us to write down an equation for the loop currents: $$ V_1(i_1,ldots,i_n) + V_2(i_1,ldots,i_n) + ldots + V_n(i_1,ldots,i_n) = 0$$ This is easy for voltage sources and resistors, but for current sources it's not possible since the voltage across a current source depends upon the circuit it is connected to.

In your circuit there is an unknown potential difference across the current source, so your original equation for M2 was incorrect as you ignored this voltage. The way to remedy this is to write an equation for a loop that doesn't include the current source (e.g. the supermesh used by Pranabendra).