Question

if a number is divided by 9 and the remainder is 6, then what is the remainder when six times this number is divided by 9?​

Answer 1

According to remainder formula:

Dividend= divisor×Quotient+ remainder

Let the number (or required number) divided by 9 be X (say divisor) and quotient be Y

Hence, according to above relation:

X= 9×Y+ 6 …….(1)

Now by 2nd condition:

X is divisible by 15

On applying remainder formula:

X= 15×Z+ 0 (where Z is the quotient)

Or, X= 15Z ……….(2)

Here, the 3rd condition is the difference between both quotients is 44 :

Y - Z = 44 (here Y>Z)

Or, Z = Y - 44 ………(3)

On solving (1), (2) & (3) we get X = 1005, Y= 111 & Z= 67

Hence, 1005 is the required number.

hope that helps uh..☺

Answer 2

SOLUTION

GIVEN

A number is divided by 9 and the remainder is 6,

TO DETERMINE

The remainder when six times the number is divided by 9

EVALUATION

Here it is given that the number is divided by 9 and the remainder is 6,

We know that

Dividend = Divisor × Quotient + Remainder

By the given

Divisor = 9

Remainder = 6

Let quotient = x

Then the number

= Dividend

= 9x + 6

Now six times the number

$\sf = 6(9x + 6)$

$\sf = 54x + 36$

$\sf = 18(3x + 2)$

Thus we see that the the number obtained 54x + 36 is completely divisible by 9

Hence the required Remainder = 0

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