Question

A bag contains 50 P, 25 P, and 10 P coins in the ratio 5:9:4, amounting to Rs. 206. Find the number of coins of each type respectively.

• A. 360, 160, 200
• B. 160, 360, 200
• C. 200, 360, 160
• D. 200, 160, 300
• E.

Hint:

When dealing with coin problems involving ratios, use a variable to represent the common multiplier and set up an equation based on the total value.

Answer 1

The Correct Option is C

Let the number of 50 P, 25 P, and 10 P coins be \( 5x \), \( 9x \), and \( 4x \) respectively, according to the given ratio of 5:9:4. The total amount in the bag is Rs. 206, which is equivalent to 20600 paise. Thus, the equation for the total value of coins is: \[ 50 \times 5x + 25 \times 9x + 10 \times 4x = 20600. \] Step 1: Simplifying the equation: \[ 250x + 225x + 40x = 20600. \] \[ 515x = 20600. \] Step 2: Solving for \( x \): \[ x = \frac{20600}{515} = 40. \] Step 3: Finding the number of each type of coin: - Number of 50 P coins: \[ 5 \times 40 = 200. \] - Number of 25 P coins: \[ 9 \times 40 = 360. \] - Number of 10 P coins: \[ 4 \times 40 = 160. \] Thus, the number of 50 P coins is 200, the number of 25 P coins is 360, and the number of 10 P coins is 160.