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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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
Question : In a division sum, the divisor is 10 times the quotient and four times the remainder. What is the dividend if the remainder is 45?
Option 1: 4123
Option 2: 3285
Option 3: 2895
Option 4: 5412
Question : In a division sum, the divisor is 13 times the quotient and 6 times the remainder. If the remainder is 39, the dividend is:
Option 1: 4240
Option 2: 4576
Option 3: 4251
Option 4: 4800
Question : In a division sum, the divisor is 10 times the quotient 'q' and five times the remainder 'r '. If r = 46, the dividend will be:
Option 1: 5042
Option 2: 5328
Option 3: 5336
Option 4: 4276
Question : When a number $x$ is divided by a divisor, it is seen that the divisor is 4 times the quotient, or double the remainder. If the remainder is 80, then the value of $x$ is:
Option 1: 6480
Option 2: 6980
Option 3: 8460
Option 4: 4680
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