How many numbers up to $500$ are divisible by $23$?

If $738 A 6 A$ is divisible by $11,$ then the value of $A$ is

$A$ number when divided by a certain divisor leaves a remainder of $241$. When twice the number is divided by the same divisor,the remainder is $112$. Find the divisor.

Let $x$ be the smallest number,which when added to $2000$ makes the resulting number divisible by $12, 16, 18$ and $21$. The sum of the digits of $x$ is

If $2 \frac{1}{2}$ is added to a number and the sum is multiplied by $4 \frac{1}{2}$,and $3$ is added to the product,and then dividing the sum by $1 \frac{1}{5}$,the quotient becomes $25$. What is the number?

$\frac{1}{16}$ of $8432 + 50 \%$ of $? = 4429$