Question:
Instead of finding \(\frac{3}{15}\) of a number, a student found \(\frac{5}{13}\) of the number. His answer was 72 more than the correct answer. Find the number.
Instead of finding \(\frac{3}{15}\) of a number, a student found \(\frac{5}{13}\) of the number. His answer was 72 more than the correct answer. Find the number.
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In fraction mistake problems, subtract the correct fraction from the wrong fraction and equate it to the given difference.
Updated On: Jul 15, 2026
- \(380\)
- \(78\)
- \(390\)
- \(150\)
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The Correct Option is C
Solution and Explanation
Concept:
The difference between the wrong fraction and correct fraction of the number is given.
Let the number be:
\[
x
\]
Step 1: Write the correct and wrong values.
Correct value: \[ \frac{3}{15}x=\frac15x \] Wrong value: \[ \frac{5}{13}x \]
Step 2: Form the equation.
Given: Wrong answer is 72 more than correct answer. \[ \frac{5}{13}x-\frac15x=72 \]
Step 3: Simplify.
Take LCM \(65\): \[ \frac{25x-13x}{65}=72 \] \[ \frac{12x}{65}=72 \]
Step 4: Find \(x\).
\[ 12x=72\times65 \] \[ x=\frac{72\times65}{12} \] \[ x=6\times65 \] \[ x=390 \] Thus, the required number is: \[ \boxed{390} \]
Step 1: Write the correct and wrong values.
Correct value: \[ \frac{3}{15}x=\frac15x \] Wrong value: \[ \frac{5}{13}x \]
Step 2: Form the equation.
Given: Wrong answer is 72 more than correct answer. \[ \frac{5}{13}x-\frac15x=72 \]
Step 3: Simplify.
Take LCM \(65\): \[ \frac{25x-13x}{65}=72 \] \[ \frac{12x}{65}=72 \]
Step 4: Find \(x\).
\[ 12x=72\times65 \] \[ x=\frac{72\times65}{12} \] \[ x=6\times65 \] \[ x=390 \] Thus, the required number is: \[ \boxed{390} \]
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