A man has Rs. 85 in coins of 2-rupee, 5-rupee and 10-rupees. The number of coins of each denomination is equal. What is the total number of coins he has?

1. A

   45

2. B

   15

3. C

   30

4. D

   60

Appeared in: DSSSB -28 August 2019 (Shift-2)

Explanation

• Let 'x' be the number of coins for each denomination (Rs. 2, Rs. 5, and Rs. 10), as the quantity is equal for all.
• The total value is represented by the equation: (2 * x) + (5 * x) + (10 * x) = 85.
• Combining the terms gives 17x = 85. Solving for x gives x = 5, which is the number of coins for each single denomination.
• The total number of coins is the sum for all three denominations: 5 (Rs. 2 coins) + 5 (Rs. 5 coins) + 5 (Rs. 10 coins) = 15 coins.

Why Other Options Were Wrong

• Option A: This is three times the correct answer. This might be chosen if one incorrectly multiplies the total number of coins (15) by the number of denominations (3).
• Option C: This would be the total number of coins if there were 10 coins of each type (3 * 10), leading to a total value of Rs. 170 (17 * 10), which is incorrect.
• Option D: This would be the total number of coins if there were 20 coins of each type (3 * 20), leading to a total value of Rs. 340 (17 * 20), which is incorrect.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving linear equations from word problems involving currency as background academic context rather than a clinical decision trigger.
• This type of problem tests logical reasoning and the ability to translate a word problem into a mathematical equation, a fundamental skill in analytical tests.
• The core skill is identifying the constant relationship (equal number of coins) and using it to build a solvable model.
• What if the total value was Rs. 119? The equation would be 17x = 119, so x = 7. The total number of coins would then be 3 * 7 = 21.

How to Approach the Question

• First, carefully read the problem to identify all the given information: the total value (Rs. 85) and the coin denominations (Rs. 2, 5, 10).
• Identify the key condition or relationship described: 'The number of coins of each denomination is equal'.
• Define a variable, such as 'x', to represent the unknown quantity, which in this case is the number of coins of each type.
• Formulate an algebraic equation that represents the total value by summing the values of each denomination (2x + 5x + 10x = 85).
• Solve the equation for 'x'. This value (x=5) is the number of coins per denomination.
• Finally, ensure you answer the specific question asked, which is the total number of coins (3 * x), not just the value of 'x'.

Concept Tested & Keywords

• Concept Tested: Solving linear equations from word problems involving currency.
• Stem keywords: Rs. 85, coins, 2-rupee, 5-rupee, 10-rupees, number of coins of each denomination is equal
• Lead-in keywords: What is the total number of coins

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