Question

A bag contains Rs. 216 in the form of one rupee, 50 paise and 25 paise coins in the ratio of 2:3: 4. The number of 50 paise coins is

• A. 96
• B. 144
• C. 114
• D. 141

Answer 1

The Correct Option is B

The correct option is (B): 144
Explanation: To solve this problem, let’s denote the number of coins as follows:
- Let the number of 1 rupee coins be \( x \).
- Let the number of 50 paise coins be \( y \).
- Let the number of 25 paise coins be \( z \).
Given that the ratio of the coins is \( x : y : z = 2 : 3 : 4 \), we can express the number of coins as:
- \( x = 2k \)
- \( y = 3k \)
- \( z = 4k \)
where \( k \) is a common multiplier.
Now, we can calculate the total value of the coins in rupees:
- Value from 1 rupee coins: \( 2k \times 1 = 2k \) rupees
- Value from 50 paise coins: \( 3k \times 0.50 = 1.5k \) rupees
- Value from 25 paise coins: \( 4k \times 0.25 = k \) rupees
Now, the total value of the coins is:
\[2k + 1.5k + k = 4.5k \text{ rupees}\]
Given that the total amount is Rs. 216, we have:
\[4.5k = 216\]
Solving for \( k \):
\[k = \frac{216}{4.5} = 48\]
Now, we can find the number of 50 paise coins:
\[y = 3k = 3 \times 48 = 144\]
Thus, the number of 50 paise coins is 144.