The total time taken by a boat to cover 400 km downstream and 320 upstream is 40 hours. If downstream speed of the boat is 4 km/hr more than upstream speed of the boat, then find the time taken (in hours) by the boat to cover 720 km downstream.

To find the time taken by the boat to cover 720 km downstream, we can break down the problem step-by-step:

Step 1: Define the variables for downstream and upstream speeds
Let the upstream speed of the boat be $u$ km/hr.
According to the problem, the downstream speed of the boat is 4 km/hr more than its upstream speed.
Therefore, the downstream speed of the boat, $d$, is:
$d=u+4$ km/hr

Step 2: Set up the equation using the total time
We are given that the total time taken to cover 400 km downstream and 320 km upstream is 40 hours.
Using the formula $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$, we can write:
$\frac{400}{d}+\frac{320}{u}=40$

Substitute $d=u+4$ into the equation:
$\frac{400}{u+4}+\frac{320}{u}=40$

Step 3: Solve the equation for $u$
Divide the entire equation by 40 to simplify it:
$\frac{10}{u+4}+\frac{8}{u}=1$

Now, find a common denominator and combine the terms:
$\frac{10u+8(u+4)}{u(u+4)}=1$
$10u+8u+32=u(u+4)$
$18u+32=u^2+4u$

Rearrange the equation into a standard quadratic form:
$u^2-14u-32=0$

Factor the quadratic equation:
$(u-16)(u+2)=0$

This gives two possible values for $u$:
$u=16$ or $u=-2$

Since speed cannot be negative, we discard $u=-2$.
Thus, the upstream speed is $u=16$ km/hr.

Step 4: Calculate the downstream speed
The downstream speed is:
$d=u+4=16+4=20$ km/hr

Step 5: Find the time taken to cover 720 km downstream
Using the downstream speed, the time taken is:
$\text{Time}=\frac{720}{20}=36$ hours

Therefore, the correct answer is 36.