A child's kiddy bank contains only Rs 1 coins, 50 paise coins and 25 paise coins. What is the total amount in the bank, given that: (1) the total number of coins is 20, and (2) the numbers of 50 paise and 25 paise coins are in the ratio 7 : 3?

Introduction / Context:
This is a classic data sufficiency question. Instead of directly calculating the amount of money, you must decide whether the given statements provide enough information to determine the total amount uniquely. The coins involved are Rs 1 coins, 50 paise coins and 25 paise coins, and the statements concern the total number of coins and a ratio between two coin types.

Given Data / Assumptions:
- The bank contains only Rs 1, 50 paise and 25 paise coins.
- Statement (1): The total number of coins is 20.
- Statement (2): The numbers of 50 paise and 25 paise coins are in the ratio 7 : 3.
- We need to know whether we can find a unique total amount from these statements.

Concept / Approach:
Let x be the number of Rs 1 coins, y the number of 50 paise coins and z the number of 25 paise coins. Statement (1) gives an equation involving x, y and z. Statement (2) gives a ratio between y and z, which we can express in terms of a single parameter. We then see whether combined statements lead to a unique solution or multiple solutions. If more than one possible combination of coin counts satisfies both statements, then the total amount cannot be determined uniquely.

Step-by-Step Solution:
Step 1: Let x = number of Rs 1 coins, y = number of 50 paise coins, z = number of 25 paise coins. Step 2: From statement (1), x + y + z = 20. Step 3: From statement (2), y : z = 7 : 3, so let y = 7k and z = 3k for some positive integer k. Step 4: Substitute into x + y + z = 20 to get x + 7k + 3k = 20, so x + 10k = 20, which gives x = 20 - 10k. Step 5: For x, y and z to be nonnegative integers, k can be 0, 1 or 2. Step 6: For k = 0: x = 20, y = 0, z = 0, total amount = 20 rupees. Step 7: For k = 1: x = 10, y = 7, z = 3, total amount = 10 * 1 + 7 * 0.5 + 3 * 0.25 = 10 + 3.5 + 0.75 = 14.25 rupees. Step 8: For k = 2: x = 0, y = 14, z = 6, total amount = 0 + 14 * 0.5 + 6 * 0.25 = 7 + 1.5 = 8.5 rupees. Step 9: Thus, multiple different total amounts (20, 14.25 and 8.5) satisfy both statements (1) and (2).

Verification / Alternative Check:
We have explicitly constructed three different valid combinations of coins satisfying all conditions. Since each gives a different total amount, the information is clearly not sufficient to fix one unique value. Trying to use only statement (1) or only statement (2) obviously produces even more possible combinations.

Why Other Options Are Wrong:
Option A is wrong because statement (1) alone gives only x + y + z = 20, which has infinitely many integer solutions and therefore cannot determine a unique amount.
Option B is wrong because the ratio alone, without the total number of coins or total amount, is insufficient.
Option C is wrong because even combining both statements leads to multiple valid solutions and multiple total amounts.

Common Pitfalls:
A common mistake is to assume that a given ratio and a total count automatically produce a unique solution, without actually checking whether variables can take multiple integer values. Another pitfall is to ignore the possibility that k can take more than one integer value in the ratio representation.

Final Answer:
Even when both statements are used together, the total amount cannot be determined uniquely, so even both statements (1) and (2) together are not sufficient to answer the question.