arpit has 21 coins consistenting of 1 and 2 rupee coins. The total value of these coins is 34 rupees. how many 1 rupee and 2 rupee coins are?

n = number of Rs2 coins
2n+(21-n) = 34
n = 13
13 Rs2 coins
8 Rs1 coins

Easy. Solve the system of equations:
a+b=21
a + 2b = 34

Let's imagine they were all 1 rupee coins. In that case, Arbit would have 21 rupees.

But instead he has 13 more than that. That means 13 of the coins must actually be 2 rupee coins.

Double-check:
8 * 1 = 8
13 * 2 = 26
--------- = -------------
21 coins = 34 rupees

Answer:
8 of the 1 rupee coins
13 of the 2 rupee coins

It's a simultaneous equation.
1 rupee coin = x
2 rupee coin = y

Arpit has 21 coins consisting of 1 and 2 rupee coins.
(i) x + y = 21

The total value of these coins is 34 rupees.
(ii) x + 2y = 34


Subtract (i) from (ii) to eliminate x
(iii) y = 13
Substiture into (i)
x + 13 = 21
x = 8
ANS 8 x 1 Rupee. 13 x 2 Rupee

___________________

Or you can substitute straight away:

Arpit has 21 coins consisting of 1 and 2 rupee coins.
(i) x + y = 21
or
(ii) x = 21 - y

The total value of these coins is 34 rupees.
(iii) x + 2y = 34
but x = 21 - y. Substitute into (iii)
21 - y + 2y = 34
y = 13
substitute into (i)
x + 13 = 21
x = 8
ANS 8 x 1 Rupee. 13 x 2 Rupee

Arpit has 21 coins consisting of 1 and 2 rupee coins.
The total value of these coins is 34 rupees.
x + y = 21
2x + y = 34
x = 13
There are 13 1- rupee and 21 2 rupee coins.