Question

A certain number when divided by 222 leaves a remainder 35. Another number when divided by 407 leaves a remainder 47. What is the remainder when the sum of these two numbers is divided by 37?​

Answer 1

Answer:

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Answer 2

The value of the remainder when the sum of  two numbers is divided by 37 is 8.

Step-by-step explanation:

Given:

When a certain number is  divided by 222 leaves a remainder 35.

When another number is  divided by 407 leaves a remainder 47.

The sum of these two numbers is divided by 37.

To Find:

The value of the remainder when the sum of these two numbers is divided by 37.

Formula Used:

Dividend = divisor x quotient + remainder

Solution:

As given- when a certain number is  divided by 222 leaves a remainder 35.

Divisor= 222    and Remainder = 35

Let the a certain number is P and  Quotient  is m.

Applying formula no.01.

$P= 222 \times m + 35$ ---------- equation no.1.

As given- When another number is  divided by 407 leaves a remainder 47.

Applying formula no.1.

Divisor=  407    and Remainder = 47

Let the a certain number is R and  Quotient  is n.

$R= 407\times n + 47$  ---------- equation no.02

As given- the sum of these two numbers is divided by 37.

The sum of these two numbers = P+R

                                                $= 222 \times m + 35+407\times n + 47$

                                                $= 37 \times6\times m + 35+37\times11\timesn\times n + 47$

Remainder when the sum of these two numbers is divided by 37

$=\frac{37 \times6\times m + 35+37\times11\timesn\times n + 47}{37}$

$=\frac{37 \times6\times m +37\times11\timesn\times n +35+47}{37}$

$=\frac{37 \times6\times m +37\times11\timesn\times n +82}{37}$

$=\frac{37 \times6\times m +37\times11\timesn\times n +2\times37+8}{37}$

$=\frac{8}{37}$

Remainder is 8.

Thus, Remainder when the sum of  two numbers is divided by 37 is 8.

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