Question

A bag contains 25-paise, 50-paise and 1-rupee coins in the ratio 4:2:5. If the total value of all the coins in the bag is Rs. 770, then find the value of all the 25 paise and 50 paise coins in the bag.

• A. Rs. 220
• B. Rs. 70
• C. Rs. 110
• D. Rs. 140

Hint:

When a problem involves ratios of quantities and a total value, the quickest method is to find the value contributed by one 'unit' of the ratio and then scale it up. Here, one ratio unit (4:2:5) has a value of \(4(25) + 2(50) + 5(100) = 100+100+500 = 700\) paise. The total value is 77000 paise, so the multiplying factor is \(77000/700 = 110\).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
We are given the ratio of the number of coins of different denominations and the total value in the bag. We need to find the combined value of two of the denominations. 
Step 2: Key Formula or Approach: 
We will represent the number of coins of each denomination using a common multiplier \(x\). Then, we will form an equation for the total value of the coins to solve for \(x\). It's best to convert all monetary values to a single unit (paise or rupees). 
Step 3: Detailed Explanation: 
Let's work with paise to avoid decimals. 1 Rupee = 100 paise. Total value = Rs. 770 = \(770 \times 100 = 77000\) paise. The ratio of the number of 25-paise, 50-paise, and 100-paise coins is 4:2:5. 

Let the number of coins be: Number of 25-paise coins = \(4x\) Number of 50-paise coins = \(2x\) Number of 100-paise (1-rupee) coins = \(5x\) 

Now, let's calculate the total value in terms of \(x\). Value of 25-paise coins = \(25 \times (4x) = 100x\) paise. Value of 50-paise coins = \(50 \times (2x) = 100x\) paise. Value of 100-paise coins = \(100 \times (5x) = 500x\) paise. 

The total value of all coins is 77000 paise. \[ 100x + 100x + 500x = 77000 \] \[ 700x = 77000 \] \[ x = \frac{77000}{700} = 110 \] The question asks for the total value of all 25 paise and 50 paise coins. Value of 25-paise coins = \(100x = 100 \times 110 = 11000\) paise. 

Value of 50-paise coins = \(100x = 100 \times 110 = 11000\) paise. Total value = Value of 25p coins + Value of 50p coins \[ \text{Total Value} = 11000 + 11000 = 22000 \text{ paise} \] Converting back to rupees: \[ \frac{22000}{100} = \text{Rs. } 220 \]
Step 4: Final Answer: 
The value of all the 25 paise and 50 paise coins in the bag is Rs. 220.