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 Concept:
This problem involves the ratio of the number of coins and their monetary value. We need to convert the coin counts into a single currency unit (Rupees).
Step 2: Key Formula or Approach:
1. Let the number of coins be \( 4x, 2x, \) and \( 5x \).
2. Total Value \( = \sum (\text{Value of one coin} \times \text{Number of coins}) \).
Step 3: Detailed Explanation:
Number of 25-paise coins \( = 4x \).
Number of 50-paise coins \( = 2x \).
Number of 1-rupee coins \( = 5x \).
Convert the values to Rupees:
25-paise \( = \text{Rs. } 0.25 \).
50-paise \( = \text{Rs. } 0.50 \).
Total value equation:
\[ (0.25 \times 4x) + (0.50 \times 2x) + (1.00 \times 5x) = 770 \] \[ 1.00x + 1.00x + 5.00x = 770 \] \[ 7x = 770 \] \[ x = 110 \] Now, find the value of 25-paise and 50-paise coins:
Value of 25-paise coins \( = 1.00x = 110 \) Rupees.
Value of 50-paise coins \( = 1.00x = 110 \) Rupees.
Total value of 25 and 50 paise coins \( = 110 + 110 = 220 \) Rupees.
Step 4: Final Answer:
The total value of all the 25 paise and 50 paise coins is Rs. 220.