A man's salary is increased by 10%. In order to have his salary back to the…
2022
A man's salary is increased by 10%. In order to have his salary back to the original amount, it must be reduced by
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Concept: When a quantity is increased by r%, restoring it to the original value is NOT the same as decreasing it by that same r% — the reduction is now taken as a percentage of the LARGER, already-increased amount, not the smaller original one. The required percentage decrease is r/(100+r) × 100.
Let the original salary be 100 units, so every step below is a plain number.
After a 10% increase, the new salary = 100 + 10 = 110 units.
To bring 110 back down to 100, the amount to cut = 110 − 100 = 10 units.
This cut of 10 units must be taken as a percentage of the CURRENT (increased) salary, 110, not the original 100: (10/110) × 100 = 1000/110 = 100/11 %.
Converting 100/11 to a mixed number: 100 ÷ 11 = 9 remainder 1, so 100/11 = 9 1/11%.
Cross-check: Reduce 110 by 9 1/11%: that cut is (100/11 × 110)/100 = 10. Subtracting gives 110 − 10 = 100, exactly the original salary — confirming the reduction.
Answer: The salary must be reduced by 9 1/11%.