Question

A number when divided by 296 leaves 75 as remainder. If the same number is divided by 37, the remainder obtained is:
$
  {\text{A}}{\text{. 2}} \\
  {\text{B}}{\text{. 1}} \\
  {\text{C}}{\text{. 11}} \\
  {\text{D}}{\text{. 8}} \\
$

Answer 1

Hint: A dividend can be written as the sum of the remainder and the product of quotient and divisor. Assume the dividend as x and then put it in this equation. The basic calculation of division is to be known and has been used in the question.

Complete step-by-step answer:
In the given question a number is divided by 296 and we get a remainder 75.
Let us assume the number or the dividend as x.
Let us assume the quotient to be y.
So, we form an equation by the formula,
Dividend = Divisor $ \times $ Quotient + Remainder
x = 296 $ \times $ y + 75
also, it is given that-
x = 37 $ \times $ y’ + r
where r is the remainder to be determined.
The first division equation can also be written as
x = (37 $ \times $ 8) $ \times $ y + 75
splitting the remainder as a factor of 37, since 37 is our point of interest
x = (37 $ \times $ 8) $ \times $ y + (37 $ \times $ 2) + 1
taking 37 common
x = 37 $ \times $ (8$ \times $ y + 2) + 1
we get the above form, which depicts that 37 is the divisor, 8 $ \times $y+2 is the quotient and 1 becomes the remainder for the dividend x.
So, if we divide the same number or dividend which we have assumed to be x here by 37 as mentioned in the question, then,
We can clearly see by the above equation that when we divide the equation by 37 we will get the remainder as 1.
The correct option is B.

Note:Since, 37 was the second divisor asked in the question and no other information was given so, if we proceeded by solving equations, we would have stuck at one point. This is why, the first divisor 296, was split as a factor of 37 and so was the remainder 75. Take a check while doing calculations.