Aptitude - Numbers - Discussion

We will first try to relate 357 and 17.

When we divide 357 by 17 reminder is 0.
That means 17 is a multiple of 357,
Hence we divide 39 by 17 reminder 5 will come.
That's the answer 5.

Formula :
Dividend = divisor * quotient + remainder.
Let dividend be n.
n=357q+39 ---> (1)
n=17q+r --> (2).
Compare (2)with (1)
So (1)should be of multiple of 17.
n = 17 * 11q + 34 + 5
n = 17(11q + 1) + 5 ---> (3).
Compare 3 with (2).
And r=5.

FORMULA :

Dividend=divisor * quotient + remainder.

Here, we ca use;
Dividend = divisor + remainder.
x = 357 + 39,
x = 396.
AB 396 DIVIDED by 17.
Then the remainder 5.

I don't understand. Please anyone explain me.

357 + 39 = 396
396 ÷ 17 (remainder is 5).

Why we are assuming quotient =1?

I am not understanding this, please help me to get it.

Thank you for this amazing solution @Rinka.

Formula: dividend=divisor*quotient+remainder.

Divisor=357, remainder=17.

So, 357*q+17.
Assume q as 1.
357+17=396.
396/17.
The remainder is 5.

Let the given num is x.
And quotient is P.

Now according to the formula, x= 357P+39 ........(i).

Again, when the same number is divided by 17, let then quotient = Q and the remainder = R
then, x = 17Q+R ...........(ii).

Now, comparing (i) & (ii) we get,
357P+39 = 17Q+R ...........(iii)
Let P=1, then, 357+39 = 17Q+R
That means, 396 = 17Q+R
Now if we divide 396 by 17, we get
396= 17 (23) + 5 ..........(iv)

Now comparing, (iii) & (iv), R=5.
So the required number is 5.