A student was supposed to multiply a number by 3/2 but instead divided the number by 3/2 (effectively multiplying by 2/3). His incorrect result was 10 less than the correct result. What was the original number?

Introduction / Context:
This classic error-analysis problem compares a correct operation with an incorrect reciprocal operation. By expressing both results in terms of the original number, the difference becomes a simple linear equation that reveals the original value.

Given Data / Assumptions:

• Original number = N.
• Correct result = N * (3/2).
• Incorrect result = N / (3/2) = N * (2/3).
• Correct result minus incorrect result = 10.

Concept / Approach:
Write the difference explicitly and solve for N. Because both expressions are proportional to N, we simply subtract the coefficients and divide to isolate N. Careful fraction arithmetic is essential to avoid sign or factor mistakes.

Step-by-Step Solution:

Verification / Alternative check:
Correct result: 12 * (3/2) = 18. Incorrect result: 12 * (2/3) = 8. Difference = 18 − 8 = 10, which matches the condition.

Why Other Options Are Wrong:
10, 15, 20, and 24 do not produce a difference of 10 between the correct and erroneous operations.

Common Pitfalls:
Dividing by 3/2 twice, mixing up which result is larger, or computing 3/2 − 2/3 incorrectly by adding denominators.

Final Answer:
12