Question

*When a number is divided by 15, the quotient is an odd number and the remainder is 1
What will be the remainder when divided by 30?

​

Answer 1

What is

• Division Algorithm?

It is literally the algorithm for division. The product of divisor and quotient, plus the remainder equals the number. In other words, $A=PQ+R$, where $P,Q,R$ are divisor, quotient, and remainder.

Solution

Let the number be $A$. Let the quotient be $Q$. Then since it is an odd number, we can write for a natural number $k$.

$\implies Q=2k+1$

Division algorithm,

$A=15Q+1$

$\implies A=15(2k+1)+1$

$\implies A=30k+15+1$

$\implies A=30k+16$

Hence, when it is divided by 30, the remainder is always $16$.

Answer 2

Question:-

• When a number is divided by 15, the quotient is an odd number and the remainder is 1.What will be the remainder when divided by 30?

To Find:-

• Find the remainder when divided by 30.

Solution:-

• Let the number be N.

According to the Question:-

$\dashrightarrow\sf \: N = 15( 2x + 1 ) + 1$

$\dashrightarrow\sf \: N = 30x + 15 + 1$

$\dashrightarrow\sf \: N = 30x + 16$

Now ,

• N is divided by 30 then the remainder is

$\dashrightarrow\sf \: 15 + 1$

$\dashrightarrow\sf \: 16$

Hence ,

• The remainder is 16 when it is divided by 30.