$a+\frac{1}{a}=3$ হলে প্রমাণ কর: $a^3+\frac{1}{a^3}=18$

A man has donated 30% of his property as charity and then gave the rest to his wife. The wife has contributed 50% of her property as charity. If wife has contributed Tk. 21,000 what was the contribution of the man as charity?

In a restaurant, the cost of an identical three-item lunch for five people was Tk. 900. The main item cost thrice as much as the desert and the desert cost twice as much as the starter. How much did the main item cost for each person?

A team of 2 men and 5 women completed one-fourth of a job in 3 days. After 3 days another man joined the team and they took 2 days to complete another one-fourth of the job. How many men can complete the whole job in 4 days?

Mr. Rahman invests Tk. 2,400 in a bank at 5% interest. How much additional money must he invest at 8% interest so that the total annual income will be equal to 6% of his entire investment?

A garden is 60 meter long and 20 meter wide. Inside the garden there is a 5 meter wide path around it. What is the area of the path in square meter?

Solve the equation: $\frac{10}{2x-5}+\frac{1}{x+5}=\frac{18}{3x-5}$

A motorist and a cyclist start from A to B at the same time. A to B is 18km. The speed of motorist is 15 m/hr, more than the cyclist. After covering half the distance, the motorist rests for 30 minutes and thereafter his speed is reduced by 20%. If the motorist reaches the destination B, 15 min earlier than that of the cyclist, then find the speed of the cyclist. 

A man can row 30 km upstream and 44 km downstream in 10 hrs. It is also known that he can row 40 km upstream and 55 km downstream in 13 hrs. Find the speed of the man in still water.

A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and Cand A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?

A vessel contains 28 liters of honey and water solution with honey and water ratio 4 : 3.21 liters of honey-water solution is added to this that his honey to water ratio as 2 : 1. Again a 51 liters honey-water solution that has honey to water ratio as 9 : 8 is added to this. After this, 10 liters of the solution is replaced with pure honey. What is ratio of water to honey in the final mixture?

A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. Find the time required by the first pipe to fill the tank?

A machine X can print one lakh books in 8 hours; machine Y can print the same number of books in 10 hours while machine Z can print them in 12 hours. All the machines are started at 9 A.M. while machine X is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work?

A man went downstream for 28km in a motor boat and immediately returned. It took the man twice as long to make the return trip. If the speed of the river flow were twice as high, the trip downstream and back would take 672 minutes. Find the speed of the boat in still water and the speed of the river flow.

Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. How many hours will take C alone to fill the tank?

Rahim has 30 marbles, 18 red & 12 blue marbles. Karim has 20 marbles. The ratio of red & blue marbles is equal to Rahim marbles. How many more blue marbles Rahim has?

A train traveling at 20 m/s completely crosses another train having 192 meters length traveling in same direction at 15 m/s in 1.5 minutes. In what time will they cross each other traveling in opposite direction and length of the faster train is?

Mr. Karim gave 40% of the money he had to his wife. He also gave 20% of the remaining amount to each of his three sons. Half of the amount now left was spent on miscellaneous items and the remaining amount of Tk. 12,000 was deposited in the bank. How much money did Mr. Karim have initially ?

A dealer buys dry fruit at the rate of Tk. 100, Tk. 80 and Tk. 60 per kg. He bought them in the ratio 12 : 15 : 20 by weight. He in total gets 20% profit by selling the first two and at last he finds he has no gain no loss in selling the whole quantity which he had. What was the percentage loss he suffered for the third quantity?

In a business A invests Tk. 600 more than B. The capital of B remained invested for $7 \frac{1}{2}$ months, while the capital of A remained invested for 2 more months. If the total profit be Tk. 620 and B gets Tk. 140 less than what A gets, then what will be the amount of A's capital?