‘A’ began a small business with a certain amount of money. After four months from the start of the business. 'B' joined the business with an amount which was Tk. 6,000 less than 'A's initial investment. 'C' joined the business after seven months from the start of business with an amount which was Tk. 2,000 less than A's initial investment. At the end of the year total investment repented was Tk. 1,42,000. What will be A's share in the profit, if 'B' received Tk. 8,000 as profit share ?

Solve the following mathematical problems:

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?

Solve the following mathematical problems:

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?

Solve the following mathematical problems:

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.

Solve the following mathematical problems:

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.

Solve the following mathematical problems:

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