A student was asked to multiply a number by 17, but by mistake he multiplied it by 71. His answer was 1296 more than the correct answer. What was the number?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 24
The wrong answer is \(71 x\) and the right one is \(17 x\); their difference is \((71-17)x\).
\(71 x-17 x=1296\)
\(54 x=1296\)
\(x=1296\div54=24\)
Check: \(24\times71=1704\), \(24\times17=408\), and \(1704-408=1296\)
The number was 24.
Why the other options are incorrect
Option (2) 26 — Incorrect. With 26, \(26\times71-26\times17=26\times54=1404\), not 1296.
Option (3) 27 — Incorrect. With 27, \(27\times71-27\times17=27\times54=1458\), not 1296.
Option (4) 22 — Incorrect. With 22, \(22\times71-22\times17=22\times54=1188\), not 1296.