There are some 50 paisa and some 25 paisa coins in a bag. If the total number of coins is 30 and their total value is ₹ 11, find the number of coins of each kind.

First, convert the total value to paisa:

₹ 1 = 100 paisa

∴ ₹ 11 = (11 × 100) paisa = 1100 paisa.

Let the number of 50 paisa coins be x.

Then, the number of 25 paisa coins = (30 - x).

Value of 50 paisa coins = 50x

Value of 25 paisa coins = 25 × (30 - x) = 750 - 25x

According to the question, total value is ₹ 11:

∴ 50x + (750 - 25x) = 1100

⇒ 50x + 750 - 25x = 1100 $\quad$ [Removing brackets]

⇒ 25x = 1100 - 750 $\quad$ [Transposing +750 to RHS]

⇒ 25x = 350

⇒ x = $\dfrac{350}{25}$

⇒ x = 14

Number of 50 paisa coins = x = 14.

Number of 25 paisa coins = (30 - x) = (30 - 14) = 16.

Hence, the number of 50 paisa coins = 14 and the number of 25 paisa coins = 16.