Error analysis on fractions: “fifth of a number” vs multiplying by its reciprocal A student should have found (2/5) of a number but instead multiplied the number by (5/2). His answer exceeded the correct one by 5208. What was the number?

Introduction / Context:This tests proportional reasoning and careful reading. The intended operation is 2/5 of N; the mistaken operation is 5/2 times N. Their difference equals 5208.

Given Data / Assumptions:

• Correct value: (2/5)N.
• Wrong value: (5/2)N.
• Wrong − Correct = 5208.

Concept / Approach:Set up a single linear equation in N using the two fractions and solve cleanly. Keep everything symbolic until the last step.

Step-by-Step Solution:(5/2)N − (2/5)N = 5208.Compute the difference factor: 5/2 − 2/5 = (25 − 4)/10 = 21/10.Thus (21/10)N = 5208 ⇒ N = 5208 * 10 / 21.Since 21 × 248 = 5208, N = 248 × 10 = 2480.

Verification / Alternative check:Correct value: (2/5)×2480 = 992; wrong value: (5/2)×2480 = 6200; difference = 5208 as required.

Why Other Options Are Wrong:2455, 2456, 2485, 2460 do not satisfy the exact fractional equation.

Common Pitfalls:Adding instead of subtracting the fractions; miscomputing 5/2 − 2/5; cancellation errors.

Final Answer:2480