Find the four angles of a cyclic quadrilateral ABCD in which ∠A=(x+y+10)°,∠B=(y+20)°,∠C=(x+y-30)° and ∠D=(x+y)°.

In a ∆ABC,∠A=x°,∠B=(3x)° and ∠C=y°. If 3y-5x=30, show that the triangle is right-angled.

The area of a rectangle gets reduced by 8 m², when its length is reduced by 5 m and its breadth is increased by 3 m. If we increase the length by 3 m and breadth by 2 m, the area is increased by 74 m². Find the length and the breadth of the rectangle.

The length of a room exceeds its breadth by 3 metres. If the length in increased by 3 metres and the breadth is decreased by 2 metres, the area remains the same. Find the length and the breadth of the room.

A part of monthly hostel charges in a college are fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 25 days, he has to pay Rs 3500 as hostel charges whereas a student B, who takes food for 28 days, pays Rs 3800 as hostel charges. Find the fixed charges and the cost of the food per day.