Question : In part one, while solving a question, Suhas accidentally took a number as a dividend which was 10% less than the original dividend. He also mistakenly took as divisor a number that was 20% less than the original divisor. If the correct quotient of the original question of division was 24 and the remainder was 0, then what quotient did Suhas obtain, assuming there was no error in his calculations?
Option 1: 27
Option 2: 21.6
Option 3: 26.4
Option 4: 30
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Correct Answer: 27
Solution :
Original quotient = 24
Original remainder = 0
Wrong dividend = 90% of original dividend
Wrong divisor = 80% of original divisor
We know that, Dividend = Divisor × Quotient + Remainder
Here, Dividend = Divisor × Quotient
So, old and new dividends, divisors and quotients are proportional
⇒ $\frac{\text{Wrong Dividend}}{\text{Original Dividend}}= \frac{\text{Wrong Divisor}}{\text{Original Divisor}}\times \frac{\text{Wrong Quotient}}{\text{Original Quotient}}$
⇒ $\frac{90}{100}= \frac{80}{100}\times \frac{\text{Wrong Quotient}}{24}$
⇒ Wrong quotient = 27
Hence, the correct answer is 27.
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