Two rabbits start running towards each other, one from A to B and another from B to A. They cross each other after one hour and the first rabbit reaches B, hour before the second rabbit reaches A. If the distance between A and B is 50 km. what is the speed of the slower rabbit? 

Pipe A can fill a tank in 18 hours, Pipe B can empty a tank in 12 hours, Pipe C can fill tank in 6 hours. The tank is already filled up to $\frac{1}{6}$ of its capacity. Now Pipe A is opened in the first hour alone, Pipe B is opened in the second hour alone and Pipe C is opened in the third hour alone. This cycle is repeated until the tank gets filled. Then in how many hours does the rest of tank get filled?

A jar contains 'x' liters of milk, a seller withdraws 25 liter of it and sells it at Tk. 20 per liter. He then replaces it water. He repeated the process total three times. Every time while selling he reduces selling price by Tk. 2. After this process milk left in the mixture is only 108 liters so he decided to sell the entire mixture at Tk. 15 per liter. Then how much profit did he earn if bought milk at Tk. 20 per liter?

A can contains milk and water in the ratio 3 : 1. A part of this mixture is replaced with milk, and now the new ratio of milk to water is 15 : 4. What proportion of original mixture had been replaced by milk?

A man rows to a place 40 km distant and back in a total of 18 hours. He finds that he can row 5 km with the stream in the same time as 4 km against the stream. What is the speed of boat in still water?

A bag contains some white and black balls. The probability of picking two white balls one after other without replacement from that bag is $\frac{14}{33}$ What will be the probability of picking two black balls from that bag if bag can hold maximum 15 balls only?

A car owner buys petrol at Tk. 75, Tk. 80 and Tk. 85 per liter for three successive years. What approximately is the average cost per liter of petrol if he spends Tk. 40,000 each year in this concern?

P is a working and Q is an investing partner. P puts in Tk. 3,40,000 and Q puts Tk. 6,50,000. P receives 20% of the profits for managerial works. The rest is distributed in proportion to their capitals. Out of a total profit of Tk. 99,000 how much does P get?

A lawn is in the form of a rectangle having its sides in the ratio 2: 3. The area of the lawn is 1/6 hectares. Find the length and breadth of the lawn.

Consider an example from a maintenance shop. The inter-arrival times of tools at that shop are exponential with an average time of 10 minutes. The length of the service time is assumed to be exponentially distributed, with mean minutes. Estimate the fraction of the day that an operator will be idle.

simplify: $\frac{x-1}{x^2-x-20}+\frac{4-x}{x^2-4x-5 }$

Prove that a parallelogram inscribed in a circle must be a rectangle.

The angle of elevation of a hot air balloon, climbing vertically from 25 degrees to 60 degrees at 10.00 am and at 10.02 am respectively. The point of observation of the angle of elevation is situated 300 meters away from the take off point. What is the upward speed (m/sec), assumed constant for the balloon?

A train 300 m long overtook a man walking along the line in the same direction of the rate of 4 km an hour and passed him in 30 second. The train reached the station in 15 minutes after it has passed the man. In what time did the man reach the station?

Two boats on opposite banks of a river start moving towards each other. They first pass each other 1,400 meters from one bank. They each continue to the opposite bank, immediately turn around and start back to the other bank. When they pass each other a second time, they are 600 meters from the other bank. We assume that each boat travels at a constant speed all along the journey. Find the width of the river?

In a mixture of milk and water, their ratio is 4 : 5 in the first container. And the same mixture has ratio 5 : 1 in the second container. In what ratio should the mixture be extracted from each container and poured into the third container, so that the ratio of milk and water comes to 5 : 4 in the third container?

A can do a piece of work in 120 days and B can do it in 150 days. They work together for 20 days. Then B leaves and A continues the work alone. 12 days after C joins A and the work is completed in 48 days more. In lion many days can C do it if he works alone?

The number of girls in a school is 160 more than $\frac{1}{3}$ of the total enrollment in the school. The number of boys is 280 more than $\frac{1}{7}$ of the total enrollment in the school. How many pupils in the school are girls?

A manufacturing company uses two machines A and B with different production capacities When working alone, machine A can produce a production lot 5 hours and machine B produce the same lot in x hours. When the two machines operate simultaneously to prod the same production lot, it takes them 2 hours to complete the job. How many hours will machine B take to produce the production lot alone?

$x+\frac{1}{x}=\sqrt{3}$ হলে, $x^6+\frac{1}{x^6}$ এর মান নির্ণয় করুন।