A student was asked to multiply a number by 38, but by mistake he multiplied it by 83. His answer was 765 more than the correct answer. What was the number?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 17
The wrong answer is \(83 x\) and the right one is \(38 x\); their difference is \((83-38)x\).
\(83 x-38 x=765\)
\(45 x=765\)
\(x=765\div45=17\)
Check: \(17\times83=1411\), \(17\times38=646\), and \(1411-646=765\)
The number was 17.
Why the other options are incorrect
Option (1) 20 — Incorrect. With 20, \(20\times83-20\times38=20\times45=900\), not 765.
Option (2) 19 — Incorrect. With 19, \(19\times83-19\times38=19\times45=855\), not 765.
Option (4) 15 — Incorrect. With 15, \(15\times83-15\times38=15\times45=675\), not 765.