In a five digit number, the digit at the hundreds place is three-fourth of the digit at ten thousands place and the digit at tens place is two-third of the digit at hundreds place. The digit at tens place is square of the smallest prime number and the digit at thousands place is the largest single digit prime number. If the digit at unit place is the largest single digit odd number, then the number is

The correct option is 87649.

Let us break down the given information step-by-step to determine each digit of the five-digit number.

Let the five-digit number be represented as:
$TKHtU$
where:
- $T$ is the digit at the ten thousands place.
- $K$ is the digit at the thousands place.
- $H$ is the digit at the hundreds place.
- $t$ is the digit at the tens place.
- $U$ is the digit at the units place.

Step 1: Find the digit at the tens place ($t$)
The problem states that the digit at the tens place is the square of the smallest prime number.
The smallest prime number is 2.
Therefore, $t=2^2=4$.

Step 2: Find the digit at the hundreds place ($H$)
The digit at the tens place ($t$) is two-third of the digit at the hundreds place ($H$):
$t=\frac{2}{3}\times H$
Substitute $t=4$ into the equation:
$4=\frac{2}{3}\times H$
$H=\frac{4\times 3}{2}=6$.

Step 3: Find the digit at the ten thousands place ($T$)
The digit at the hundreds place ($H$) is three-fourth of the digit at the ten thousands place ($T$):
$H=\frac{3}{4}\times T$
Substitute $H=6$ into the equation:
$6=\frac{3}{4}\times T$
$T=\frac{6\times 4}{3}=8$.

Step 4: Find the digit at the thousands place ($K$)
The digit at the thousands place is the largest single-digit prime number.
The single-digit prime numbers are 2, 3, 5, and 7. The largest among them is 7.
Therefore, $K=7$.

Step 5: Find the digit at the units place ($U$)
The digit at the units place is the largest single-digit odd number.
The single-digit odd numbers are 1, 3, 5, 7, and 9. The largest among them is 9.
Therefore, $U=9$.

Step 6: Combine all the digits
- Ten thousands place ($T$) = 8
- Thousands place ($K$) = 7
- Hundreds place ($H$) = 6
- Tens place ($t$) = 4
- Units place ($U$) = 9
Putting the digits together gives the five-digit number: 87649.