$if x=y^a, y=z^b and z=x^c,$ then the value of abc is

To fill an art exhibit, the students in an art course are assigned to create one epiece of artwork each in the following distribution $\frac{1}{3}$ are sculptures, $\frac{1}{8}$are oil paintings are water colours and the remaining 10 pieces are mosaics. How many students are in the art class?

A man covers a certain distance on a toy train. Had the train moved 4 km/hr faster, it would have taken 30 minutes less. If it moved 2 km/hr slower, it would taken 20 minutes more. Find the distance.

Machine A, working alone at its constant rate, produces x pounds of peanut butter in 12 minutes. Machine B, working alone at its constant rate, produces x pounds of peanut butter in 18 minutes. How many minutes will it take machines A and B, working simultaneously at their respective constant rates, to produce x pounds of peanut butter?

Tow trains running at the rate of 75km and 60km an hour respectively on parallel rails in opposites directions, are to pass each other in 8 seconds and when they are running in the same direction at the same rates as before, a person sitting in the faster train observes that he passes the other in 33$\frac{1}{2}$ seconds. Find the lengths of the trains.

pot contains 81 litres of pure milk $\frac{1}{3}$ of liters of the milk is replaced by the same amount of water. Again $\frac{1}{3}$ of the mixture is replaced by that amount of water. Find the ratio of milk and water in the new mixture.

A train 400 meter long overtook a man walking along the line in the same direction at a speed of 5 km/hr and passed him in 40 seconds. The train reached the station in 20 minutes after it had passed the man. In what time did the man reach the station?

The speed of the boat in still water is 24 kmph and the speed of the stream is 4 km/hr. The time taken by the boat to travel from A to B downstream is 36 minutes less than the time taken by the same boat to travel from B to C upstream. If the distance between A and B is 4km more than the distance between B and C, what is the distance between A and B?

A and B are two stations 390km apart. A train starts from A at 10am and travels towards Bat 65 kmph. Another train starts from B at 11 and travels towards A at 35 kmph at what time do they meet.

A box contains 75 rods; 35 are blue and 25 of these blue rods are twisted at the bottom. Th rest of them are red and 30 of the red ones are twisted. The rods that are not twisted are clear, What is the probability of drawing?

The sum of race times of two runners is 170 seconds. One of the runners took ten seconds Jess than twice the other to complete the race. What is the race time of each runner?

Shakib is twice as old as Fahim. Four years ago, Shakib was six years younger than three times of Fahims age at that time. How old will they be in two years from now?

Four students contributed to a charity drive and the average amount contribution by each student was BDT 20. If no student gave more than BDT 25, what is the minimum amount that any student could have contributed?

The sum of 15 consecutive integers is 88. What is the largest of these integers?

$x^2-12x+27<0$

$x^2-13x+40\ge 0$

A school has 40 rooms that can sit 600 people. Some rooms can sit 10 people and some cu sit 20 people. What is the ratio of the number of 10 person rooms to the number of 20 persu rooms?

B Out of 85 football players, 42 have scored a goal and 54 have received a yellow card. If 5 players did not do either, what fraction of the players scored a goal and received a yellow card as well?

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?

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