Mathematics:

If 9 engines consume 24 metric tones of coal, when each is working 8 hours a day, how much coal will be required for 8 engines, each running 13 hours a day, it being given that 3 engines of former type consume as much as 4 engines of latter type?

Solve the following mathematical problems:

A place of stone fell from a balloon when it was flying in the upward direction with a velocity 20 m/sec. What will be the height of the balloon when the stone hit the ground in 10 seconds?

Solve the following mathematical problems:

Find the maximum value of z=6x+2y, subject to the conditions $x\ge 0, y\ge 0, x+y=5, x\le 2, y\le 4.$

Solve the following mathematical problems:

The sum of the digits of a two-digit number is subtracted from the number. How two-digit numbers can be formed so that the digit in the unit place of the resulting number many such 6?

Solve the following mathematical problems:

How many ways are there to divide 50 people into 3 groups so that each group contains members equal to a prime number?

Solve the following mathematical problems:

A semi circular sheet of metal of diameter 28 cm is bent into an open conical cup. Find the depth and capacity of cup.