A bag contains three types of coins — 1-rupee coins, 50 p-coins and 25 p-coins totalling 175 coins. If the total value of the coins of each kind be the same, the total amount in the bag is

### Concept & Logic This problem introduces an inverse relationship constraint: instead of the *number* of coins being equal, the *total value* contributed by each denomination is equal. If the value is constant, lower denominations require proportionally more coins to reach that same value. ### Step-by-Step Solution * **Given:** Total coins = 175. Denominations = ₹ 1, 50p (₹ 0.50), 25p (₹ 0.25). The total monetary value contributed by each type is identical. * **Calculation:** Let the total value contributed by each specific denomination be ₹ $V$. * Because each of the 3 types contributes ₹ $V$, the total amount in the bag is $3V$. Our goal is to find $V$. * Number of ₹ 1 coins needed to make ₹ $V$ = $\frac{V}{1} = V$ * Number of 50p coins needed to make ₹ $V$ = $\frac{V}{0.50} = 2V$ * Number of 25p coins needed to make ₹ $V$ = $\frac{V}{0.25} = 4V$ * The total number of coins is the sum of these quantities: $$V + 2V + 4V = 175$$ $$7V = 175$$ $$V = 25$$ * Each denomination contributes ₹ 25 to the bag. * Total amount in the bag = $3 \times V = 3 \times 25 = 75$. ### Exam Strategy & Shortcut Since the value of each coin type is the same, the ratio of the *number of coins* is simply the inverse of their *face values*. Face values ratio: 1 : 1/2 : 1/4. Coin quantities ratio: 1 : 2 : 4. Total ratio parts = $1 + 2 + 4 = 7$ parts. 7 parts = 175 coins $\implies$ 1 part = 25 coins. Since the "1 part" corresponds to the ₹ 1 coins, there are 25 ₹ 1 coins, which are worth ₹ 25. Since all 3 types have equal value, total amount = $25 \times 3 = 75$. ### Common Pitfall Calculating $V = 25$ and immediately looking for 25 in the options. Remember that $V$ is the value of just *one* denomination type. You must multiply by 3 to get the total amount in the bag. ### Final Answer **Therefore, the correct answer is ₹ 75.**