Question

I have one-rupee coins, 50-paisa coins and 25-paisa coins. The number of coins are in the ratio 2.5 : 3 : 4. If the total amount with me is Rs. 210, find the number of one-rupee coins.

• A. 90
• B. 85
• C. 100
• D. 105

Hint:

Use ratios to express variables in terms of others and solve equations systematically.

Answer 1

The Correct Option is C

Let the number of one-rupee coins be \( x \), the number of 50-paisa coins be \( y \), and the number of 25-paisa coins be \( z \). The ratio of the number of coins is given as: \[ \frac{x}{y} = \frac{2.5}{3} = \frac{5}{6}, \quad \frac{y}{z} = \frac{3}{4}. \] Thus, \( x = \frac{5}{6} y \) and \( y = \frac{3}{4} z \). The total amount is Rs. 210. The value of the one-rupee coins is \( x \), the value of the 50-paisa coins is \( \frac{y}{2} \), and the value of the 25-paisa coins is \( \frac{z}{4} \). Therefore: \[ x + \frac{y}{2} + \frac{z}{4} = 210. \] Substitute \( x = \frac{5}{6} y \) and \( y = \frac{3}{4} z \) into this equation: \[ \frac{5}{6} y + \frac{y}{2} + \frac{z}{4} = 210. \] Solving this equation gives \( x = 100 \).