Error-analysis in fraction operations: A boy was instructed to multiply a given number by 8/17. Instead, he divided the number by 8/17 (i.e., multiplied by 17/8) and thus obtained a result that was 225 more than the correct product. What was the original number?

Introduction / Context:
This problem checks understanding of how dividing by a fraction compares to multiplying by that fraction, and how to set up an equation from a stated excess (the result is 225 more). It is a classic error-analysis question common in aptitude tests on fractions.

Given Data / Assumptions:

• The intended operation is multiply by 8/17.
• The mistaken operation is divide by 8/17, which equals multiply by 17/8.
• The mistaken result exceeds the correct result by 225.
• Let the original number be x.

Concept / Approach:
Translate the narrative into algebraic expressions for both the correct and mistaken results, then equate their difference to 225. Use a ÷ (p/q) = × (q/p). Solve the linear equation cleanly by clearing denominators.

Step-by-Step Solution:
Correct result = x * (8/17).Mistaken result = x ÷ (8/17) = x * (17/8).Excess = (x * 17/8) − (x * 8/17) = 225.Compute the bracket: 17/8 − 8/17 = (289 − 64)/136 = 225/136.So x * (225/136) = 225 ⇒ x = 225 * (136/225) = 136.

Verification / Alternative check:
Plug x = 136: correct = 136 * 8/17 = 64; mistaken = 136 * 17/8 = 289; difference = 289 − 64 = 225, matching perfectly.

Why Other Options Are Wrong:
8 and 17 are much too small; 64 is the correct result, not the original number; 272 doubles the true value and violates the 225 difference.

Common Pitfalls:
Forgetting that dividing by 8/17 multiplies by 17/8; subtracting in the wrong order; arithmetic slips when finding 17/8 − 8/17.

Final Answer:
136