Question

A number when divided by 432 leaves 85 as remainder. If the same number is divided by 36, then find the remainder.
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Answer 1

Answer:

A number when divided by 342 leaves a remainder of 47. What would be the remainder, if the same number is divided by 19?

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*(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...!!