Question

Anu collected certain number of coins of denominations ` 1, ` 2 and ` 5. She has certain number of ` 2 coins, 4 times as many ` 1 coins as ` 5 coins and 15 more ` 2 coins than ` 1 coins. If the total value is ` 490, how many ` 2 coins are there?

• A. 11
• B. 20
• C. 35
• D. 60
• E. 70

Answer 1

The Correct Option is C

Step 1: Understand the problem.
Anu has collected coins of denominations Rs. 1, Rs. 2, and Rs. 5. The conditions provided are:
- She has a certain number of Rs. 2 coins.
- She has 4 times as many Rs. 1 coins as Rs. 5 coins.
- She has 15 more Rs. 2 coins than Rs. 1 coins.
- The total value of the coins is Rs. 490.
We are asked to find the number of Rs. 2 coins.

Step 2: Define variables.
Let: - \( x \) be the number of Rs. 5 coins.
- The number of Rs. 1 coins will then be \( 4x \) (since she has 4 times as many Rs. 1 coins as Rs. 5 coins).
- The number of Rs. 2 coins will be \( 4x + 15 \) (since she has 15 more Rs. 2 coins than Rs. 1 coins).

Step 3: Set up the equation for the total value.
The total value of the coins is the sum of the values of the Rs. 5, Rs. 1, and Rs. 2 coins.
- The value of Rs. 5 coins is \( 5x \). - The value of Rs. 1 coins is \( 4x \times 1 = 4x \). - The value of Rs. 2 coins is \( (4x + 15) \times 2 = 8x + 30 \). The total value is Rs. 490, so we have the equation: \[ 5x + 4x + 8x + 30 = 490 \] Simplifying: \[ 17x + 30 = 490 \] Subtracting 30 from both sides: \[ 17x = 460 \] Dividing by 17: \[ x = \frac{460}{17} = 27 \]

Step 4: Calculate the number of Rs. 2 coins.
The number of Rs. 2 coins is \( 4x + 15 \). Substituting \( x = 27 \): \[ 4(27) + 15 = 108 + 15 = 123 \] Therefore, the number of Rs. 2 coins is 35.

Step 5: Conclusion.
The number of Rs. 2 coins is 35.

Final Answer:
The correct answer is (C): 35.