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I am wondering that how can current be equal on either side of a resistor as the work of a resistor is to resist the flow of electrons i.e. decrease the current. How is this possible?

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It decreases the potential, not the current. Think of a straw or a hose. The amount of fluid flowing in one end is the same amount that flows out the other end. –  Brandon Enright May 25 at 5:36

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The term decrease in resistors decrease current doesn't mean the outflow is smaller than the inflow. It means the flow through that entire channel/pipe/wire is smaller with the resistor than without.

It's probably more accurate to think of a resistor as impeding or restricting current. Like a kink in an air hose or water hose. The flow just before & just after the kink will be smaller than without the resistor. But the same amount of stuff that flows into the kink/resistor also flows out; otherwise stuff would be accumulating inside the resistor.

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I agree with you that what goes in should come out but the speed at which they come may be slower then with which they enter –  Ayaan J May 25 at 5:15
    
That could be true, and it does happen even with water or air when flowing from a thin pipe to a thick one (or vice versa). The speed changes. But what doesn't change is the amount of stuff per unit time. The mass of water per second, the number of Coulombs per second, etc. –  BMS May 25 at 5:19
    
By speed I actually meant the no. of coulombs per second. The resistor increases the time taken by charges to flow through a given point per unit time. So by this there should be a decrease in current. –  Ayaan J May 25 at 5:28
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Think about what happens when you add a kink somewhere in the middle of a hose that has water flowing through it. The flow of water coming out of the end of the hose decreases. But the water flowing through every part of the hose decreases too, even the part of the hose that is before the kink. The kink or resistor affects the flow everywhere in the pipe, not just "downstream". –  BMS May 25 at 6:39

Charge is a conserved quantity. If charge flows into a resistor at 1 charge unit per second, it must also flow out at 1 charge unit per second.

Liken the circuit/resistor system to a smooth tile floor where one of the tiles has been covered in sandpaper. Now imagine you have a bunch of wood blocks all attached to each other with rope to form a chain of wood blocks, and you are dragging this chain of wood blocks across the floor.

There's going to be friction between the sandpaper part of the floor and whatever block is being dragged across it at that time, but all of the blocks still move at the speed with which you are dragging them. That's kind of how it is in a circuit.

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Then what is the work of a resistor? –  Ayaan J May 25 at 5:18
    
The work of the resistor is energy absorbed from the current of electrons. Because the resistor resists the current, some of the kinetic energy of the electron flow is dissipated as heat. In terms of the example I drew up for you, the work of the resistor (sandpaper section of floor) is the heat created by friction between the sandpaper and the wood blocks. You can still drag the blocks across sandpaper just as fast as you can drag them across a smooth surface, it just takes more work on your part. This extra work on your part is the heat created by friction, or the work of the resistor. –  Rick Sanchez May 25 at 5:31

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