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Using the concept of division works really well in such questions. It is good to remember that division is nothing but grouping. So when I say that a number is divided by 342, it means I split that number into groups of 342 and 47 was leftover. 342 is divisible by 19 so when you divide the same number by 19, every group of 342 will be cleanly split in groups of 19 and nothing will be left over. (This is what happens in most such cases.) We only need to worry about the leftover 47. You can split 47 in two groups of 19 and then 9 will be leftover. Hence your remainder here will be 9.

(Note: For further clarity, refer to the theory of division.)
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i tried it in da foll way.. x=342q + 47 taking least possible way suppose q=1 ,then x is 347+47 =389 hence x = 19p + z try dividing 389 by 9 ,u get remainder 9..

i tried it in da foll way.. x=342q + 47 taking least possible way suppose q=1 ,then x is 347+47 =389 hence x = 19p + z try dividing 389 by 9 ,u get remainder 9..

This approach is fine though the least possible such number is 47 (q = 0). To understand how to figure it out orally, check out the blog post:

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

There are generally one common thing among almost all such questions i.e. First Divisor (342 in this case) will be a Multiple of Second Divisor (19 in this case). i.e. Remainder with first divisor will always be the remainder with second divisor

Since 342 is a multiple of 19 therefore If Remainder when Number divided by 343 is 47 then, Remainder when Number divided by 19 will be 47 (which can further be divided to finally calculation the final remainder) = Remainder (47/19)=9

Another method is to find a number that satisfies the first condition and calculate the remiainder with second divisor

i.e. Number when divided by 342 gives remainder 47 i.e. one of the numbers of such tyoe can be 342+47 = 389 now divide 389 by 19 and see the remainder Remainder (47/19)=9 Final Remainder
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