Solve the following mathematical problems:

A basin can be filled by tap A in 5 hours and tap B in 8 hours, each tap working on its own When the basin in full and a drainage hole is open, the water is drained in 20 hours. If initially the basin was empty and someone started the two taps together but left the drainage hole open, how long does it take for the basin to be filled?

solve the following mathematical problem:

A family has 480kg of rice for X number of weeks. If they need to use the same amount for 4 more weeks, they need to cut down their weekly assumption of rice by 4kg. What is the value of X?

solve the following mathematical problem:

if $\cos \left(A+B\right)=\frac{1}{\sqrt{2}} and \cos \left(A-B\right)=\frac{\sqrt{3}}{2}, 0^{\circ }<\left(A+B\right)\le {90}^{\circ } and A>B, find the value of A and B.$

solve the following mathematical problem:

A shopkeeper sells two shirts at the same price. He makes 10% profit on one and loses 10% the other. How much in percentage does he gain or lose?

solve the following mathematical problem:

$if a=x{y}^{p-1}, b=x{y}^{q-1}, c=x{y}^{r-1} and p+q+r=3, then prove that a^{q-r}\times b^{r-p}\times c^{p-q}=1$

solve the following mathematical problem:

Price of 3 tables and 5 chairs is Tk. 2,000. Again, price of 5 tables and 7 chairs is Tk 3,200. What is the price of 1 table and 1 chair?