Question

Remainder of a number is 3 and 2 when divided by 5 and 7 respectively. What will be the remainder of the same number if divided by 35 ?

#Please give correct answer..​

Answer 1

ANSWER :

Let the number be "n".

So by the relation

Dividend = divisor × quotient + remainder

n = 5x + 3

7n = 35x + 21 ... ( 1 ) multiplied

by 7

n = 7y + 2

5n = 35y + 10 ... ( 2 ) multiplied

by 5

subtracting eqn ( 2 ) from eqn ( 1 )

2n = 35 ( x - y ) + 11 ... ( 3 )

subtracting eqn ( 3 ) from eqn ( 2 )

3n = 35 ( 2y - x ) - 1 ... ( 4 )

Subtracting eqn ( 3 ) from eqn ( 4 )

n = 35( 3y - 2x ) - 12 ... ( 5 )

n = 35 ( 3y - 2x ) + 35 - 35 - 12

n = 35 ( 3y - 2x - 1 ) + 35 - 12

n = 35 ( 3y - 2x - 1 ) + 23

HENCE THE ANSWER IS 23.

THANKS!!!!!!!!

Answer 2

The number would be 23 and the remainder would be 12. I’ll elaborate:

I saw this similar question and an answer there showed a formula of his: (link below)

Dividend = (Quotient * Divisor) + Remainder

Terms:

Dividend - 1st number in a division; numerator

Quotient - answer in a division

Divisor - 2nd number in a division; denominator

Remainder - excess number from the quotient (if whole number) of a division.

There are two equations given in the first sentence of the problem:

First Equation: N = Q1(5) + 3

Second Equation: N = Q2(7) + 2

We give values to Q1:

Q1 = 1, 2, 3, 4,…

We subsitute these values in the first equation to give N possible values.

(First Equation) N = 8, 13, 18, 23,…

After giving N values, we give Q2 the same values as Q1, substitute it to the second equation and find common N values.

Q2 = 1, 2, 3,..

(Second Equation) N = 9, 16, 23,…

Here, we notice that both equations has 23 as the value of their N. This means that 23 is “that number”.

Now, we divide the number, 23, by 35 to find its remainder. The remainder would be 12, answering the question.

plz plz plz can be your friend