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 determine the digit at each place value of the five-digit number step-by-step from the given information.
Let the five-digit number be represented as T Th Th H T U, where:
- T Th is the digit at the ten thousands place,
- Th 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 smallest prime number is 2.
The digit at the tens place is the square of the smallest prime number:
$T=2^2=4$

Step 2: Find the digit at the hundreds place (H)
It is given that the digit at the tens place is two-third of the digit at the hundreds place:
$T=\frac{2}{3}\times H$
Substituting $T=4$ 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 Th)
It is given that the digit at the hundreds place is three-fourth of the digit at the ten thousands place:
$H=\frac{3}{4}\times \mathrm{T\; Th}$
Substituting $H=6$ into the equation:
$6=\frac{3}{4}\times \mathrm{T\; Th}$
$\mathrm{T\; Th}=\frac{6\times 4}{3}=8$

Step 4: Find the digit at the thousands place (Th)
The single digit prime numbers are 2, 3, 5, and 7.
The largest single digit prime number is 7.
So, the digit at the thousands place is:
$\mathrm{Th}=7$

Step 5: Find the digit at the units place (U)
The largest single digit odd number is 9.
So, the digit at the units place is:
$U=9$

Conclusion:
Combining all the digits together in their respective place values:
- Ten thousands place (T Th) = 8
- Thousands place (Th) = 7
- Hundreds place (H) = 6
- Tens place (T) = 4
- Units place (U) = 9

Therefore, the required five-digit number is 87649.