Section E : Mathematics (Qs. 24-28)

A ship 77 km from the shore, springs a leak which admits $2\frac{1}{4}$ tones of water in $5\frac{1}{2}$ minutes. 92 tones of water would sink it. But the pumps can throw out 12 tons of water per hour. Find the average rate of sailing so that the ship may just reach the shore as it begins to sink.

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?