Question : During a division, Pranjal mistakenly took as the dividend a number that was 10% more than the original dividend. He also mistakenly took as the divisor a number that was 25% more than the original divisor. If the correct quotient of the original division problem was 25 and the remainder was 0, what was the quotient that Pranjal obtained, assuming his calculations had no error?
Option 1: 21.75
Option 2: 21.25
Option 3: 28.75
Option 4: 22
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Correct Answer: 22
Solution :
Given:
Original quotient = 25
Original remainder = 0
Let, original dividend be $x$ and divisor be $y$.
We know, Dividend = Quotient × Divisor + Remainder
So, for the number, $25y+0=x$
⇒ $25y=x$
He mistakenly took as the dividend a number that was 10% more than the original dividend.
So, the new dividend is $\frac{110x}{100}=\frac{110×25y}{100}$.
He also mistakenly took as the divisor a number that was 25% more than the original divisor.
So, new divisor = $\frac{125y}{100}$
So, new quotient = $\frac{\frac{110×25y}{100}}{\frac{125y}{100}}=22$
So, the quotient that Pranjal obtained, assuming his calculations had no error is 22.
Hence, the correct answer is 22.
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