Question

A number when divided by 342 gives a remainder 47. When the same number is divided by 19, what would be the remainder?

Answer 1

Hint: We have given that when a number is divided by 342 it gives 47 as a remainder. Let us write this statement in the form of dividend, divisor, quotient and remainder. The relation between these terms is equal to $\text{Dividend}=\text{Divisor}\times \text{Quotient}+\text{Remainder}$. Now, 342 is the divisor, 47 is the remainder, Dividend is the number given and let us assume that quotient is “q” and then substitute these values in the formula. After that, rearrange the equation in such a way that the equation will reduce in the form of some constant multiplied by 19. Then the remaining term in the expression other than 19 is the remainder.

Complete step-by-step answer:
We know the relation between dividend, divisor, quotient and remainder as follows:
$\text{Dividend}=\text{Divisor}\times \text{Quotient}+\text{Remainder}$
Now, we have given that a number when divided by 342 gives a remainder 47. According to the formula, 342 is the divisor, 47 is the remainder, and dividend is the given number and let us assume that quotient is “q”. Substituting all these values in the above formula we get,
$\text{Given number}=342\times q+47$
In the next half of the problem, we have to find the remainder when the same number is divided by 19 so we are going to manipulate the above expression as follows:
$\text{Given number}=19\times 18q+19\times 2+9$
Taking 19 as common from the first two terms of the expression written on the L.H.S of the above equation we get,
$\text{Given number}=19\times \left( 18q+2 \right)+9$
If you carefully look at the above equation, you will find that 19 is the divisor, given number is dividend and 9 is the remainder and quotient is 18q + 2. This mathematical expression is equivalent to the other half of the question which says that “when the same number is divided by 19” and we are asked to find the remainder so the remainder is equal to 9.
Hence, when the same number is divided by 19 we got the remainder as 9.

Note: This question demands the knowledge of the relation between dividend, divisor, quotient and remainder which we have shown above as:
$\text{Dividend}=\text{Divisor}\times \text{Quotient}+\text{Remainder}$
If you don’t know the above relation, it will be nearly impossible to solve this problem. Along with that in the second half of the question, you should use your brain apart from just using the above formula to get the answer.