Question

A no when divided by 342 gives a remainder 47. when the same no. divided by 19 what would be the remainder

Answer 1

As per statement 1, 
The number must be of the form  342k + 47 , where k is any integer
(Try recalling what you read in younger classes, i.e.
Dividend=Divisior*Quotient+Remainder)

Here;
Dividend is the number itself
Divisior is 342
Remainder is 47
Quotient obviously would be any integer (let it be k)

Now, further 
342k + 47 = 19*18k + (38+9) 
= 19*18k + 19*2 + 9
(19*2 when divided by 19 gives the quotient 2)
= 19*(18k+2) + 9
= 19m + 9 (here m is any other integer)

Now again recall that
Dividend=Divisior*Quotient+Remainder

Here;
Dividend is the number itself
Divisior is 19
Quotient is m (obviously an integer)
Remainder is 9....!!

Hope this helps you with your problem...!! 
Cheers...!!