When 4150 is divided by a certain number, the quotient is 55 and the remainder is 25. What is the value of the divisor?

Introduction / Context:
This question uses the basic relation between dividend, divisor, quotient and remainder. It checks whether candidates can work backward from quotient and remainder to find the original divisor. Such problems are fundamental in number system topics and appear frequently in exams.

Given Data / Assumptions:
Dividend (original number) = 4150.Quotient = 55.Remainder = 25.We must determine the divisor.

Concept / Approach:
The standard relation in division is Dividend = Divisor * Quotient + Remainder. If we know three of these quantities, we can solve for the fourth. Here we know the dividend, quotient and remainder. Substituting into the formula allows us to isolate the divisor and compute it directly.

Step-by-Step Solution:
Step 1: Use the division identity: Dividend = Divisor * Quotient + Remainder.Step 2: Substitute the values: 4150 = Divisor * 55 + 25.Step 3: Subtract the remainder from both sides to isolate the multiple of the divisor: 4150 − 25 = Divisor * 55.Step 4: Compute the left side: 4150 − 25 = 4125.Step 5: Now we have 4125 = Divisor * 55.Step 6: Solve for the divisor by dividing both sides by 55: Divisor = 4125 / 55.Step 7: Perform the division: 4125 / 55 = 75.Step 8: Therefore, the divisor is 75.

Verification / Alternative check:
Check the result by performing the division using the found divisor. If we divide 4150 by 75, we get 75 * 55 = 4125 and the remainder 4150 − 4125 = 25, which exactly matches the given quotient and remainder. This confirms that our calculation of the divisor is correct.

Why Other Options Are Wrong:
For divisor 65, the product 65 * 55 = 3575, and adding the remainder 25 gives 3600, which is not 4150. For divisor 68, the product 68 * 55 = 3740; adding 25 gives 3765, again incorrect. For divisor 70, 70 * 55 = 3850, and 3850 + 25 = 3875, still not equal to 4150. Only 75 satisfies the division identity correctly.

Common Pitfalls:
Some learners mistakenly divide the dividend by the quotient and ignore the remainder, which leads to an incorrect value. Others try to guess a divisor from the options without applying the formula systematically. Remembering and using the relation Dividend = Divisor * Quotient + Remainder avoids such errors.

Final Answer:
The required divisor is 75.