Section E : Mathematics (Qs. 24-28)

In the figure, what is the area of $∆ABC if \frac{EC}{ED} =3 ?$ 

Solve the followings:

Simplify: $\left[\left(3-x\right)\left(x+2\right)+\left(-x+4\right)\left(7x+2\right)-\left(x-y\right)\left(2x-y\right)\right]-3x^2-7x+5$

Solve the followings:

A salesman sells two shirts at BDT 594 each. On one he gains 10% and on the other, he loses 10%. Find his gain or loss percent on the whole.

Solve the followings:

A solution made up of 40% alcohol by volume is mixed with 4 liters of solution that is 10% alcohol by volume. How much, in liters of the 40% alcohol solution is needed to make a mixture that is 25% alcohol by volume?

Solve the followings:

If 24 machines can make 5 devices in 30 minutes, how many hours will it take 4 machines to make 15 devices?

Solve the followings:

An equilateral triangle is inscribed into a circle with radius 10cm. What is the area of the triangle?