Question

A bag has Rs.785 in the denomination of Rs. 2, Rs.5 and Rs.10 coins.The coins are in the ratio of 6:9:10. How many coins of Rs.5 are in the bag:

• A. 60
• B. 12
• C. 45
• D. 24

Answer 1

Answer:

C. 45

Understanding the Problem

This problem involves calculating the number of coins of a specific denomination given the total value of coins, the denominations present, and the ratio of the number of coins of each denomination.

Key Concepts Involved:

• Ratio: A comparison of two or more quantities.
• Total Value: The sum of the values of all the coins.
• Denominations: The face value of the currency (e.g., Rs. 2, Rs. 5, Rs. 10).

Steps to Solve:

1. Represent the number of coins: Since the coins are in the ratio 6:9:10, let the number of Rs. 2, Rs. 5, and Rs. 10 coins be 6x, 9x, and 10x respectively.
2. Calculate the value of each denomination:
   • Value of Rs. 2 coins = (Number of Rs. 2 coins) imes (Face value of Rs. 2 coin) = 6x imes 2 = 12x
   • Value of Rs. 5 coins = (Number of Rs. 5 coins) imes (Face value of Rs. 5 coin) = 9x imes 5 = 45x
   • Value of Rs. 10 coins = (Number of Rs. 10 coins) imes (Face value of Rs. 10 coin) = 10x imes 10 = 100x
3. Form an equation for the total value: The sum of the values of all denominations equals the total amount in the bag.

   12x + 45x + 100x = 785

4. Solve for 'x': Combine the terms on the left side of the equation.

   157x = 785

   Divide both sides by 157:

   x = 785 / 157

   x = 5

5. Calculate the number of Rs. 5 coins: The number of Rs. 5 coins is represented by 9x. Substitute the value of x found in the previous step.

   Number of Rs. 5 coins = 9 imes 5

   Number of Rs. 5 coins = 45

Exam-Oriented Points:

• Problems involving ratios and total values are common in competitive exams.
• Carefully identify the ratio and the denominations given in the question.
• Ensure accurate calculation of the value contributed by each denomination.
• The variable 'x' represents a common multiplier for the ratio.