Shaan received Rs. 912 in equal numbers of Rs. 1, Rs. 5 and Rs. 10 coins. How many coins does Shaan have in total?

Introduction / Context:
This arithmetic question is about money distribution and simple linear equations. Shaan has coins of three different denominations, and the question states that the number of coins of each denomination is equal. We are asked to calculate the total number of coins given the overall amount of money.

Given Data / Assumptions:

• Total amount of money = Rs. 912.
• There are equal numbers of Rs. 1, Rs. 5 and Rs. 10 coins.
• We must find the total count of coins.

Concept / Approach:
Let the number of coins of each type be n. Then there are n coins of Re. 1, n coins of Rs. 5 and n coins of Rs. 10. The total value is then a simple expression in n, which we equate to 912. Solving for n gives the count for each denomination, and multiplying by three gives the total number of coins.

Step-by-Step Solution:
Step 1: Let n be the number of coins of each denomination. Step 2: The total value of Re. 1 coins is 1 * n = n rupees. Step 3: The total value of Rs. 5 coins is 5n rupees. Step 4: The total value of Rs. 10 coins is 10n rupees. Step 5: The overall total value is n + 5n + 10n = 16n. Step 6: Set 16n equal to 912: 16n = 912. Step 7: Solve for n: n = 912 / 16 = 57. Step 8: The total number of coins is 3n = 3 * 57 = 171.

Verification / Alternative check:
Check by computing the actual amount using the obtained n. With 57 coins of each type, the amount from Re. 1 coins is Rs. 57, from Rs. 5 coins is Rs. 285 and from Rs. 10 coins is Rs. 570. The total is 57 + 285 + 570 = 912, which matches the given amount.

Why Other Options Are Wrong:

• Option A: 16 coins would correspond to a very small total amount, far less than Rs. 912.
• Option B: 57 coins would mean only one set, not the combined total of three sets.
• Option D: 323 coins does not correspond to a total value of Rs. 912 when coins are equally split among three denominations.
• Option E: 192 coins also gives a different total amount when split equally among three types.

Common Pitfalls:
A common mistake is to set 1 + 5 + 10 equal to 912 and to forget that each denomination appears n times. Another error is to think that 57 is the total number of coins instead of the number for each denomination. Introducing a variable for the number of coins and writing the total value explicitly helps to avoid such confusion.

Final Answer:
Shaan has a total of 171 coins.