Commission, Brokerage and Discount

If the difference between true discount and banker's discount on a sum due 4 months hence is Rs 20,  find true discount, banker's discount and amount of the bill, the rate of simple interest charged being 5% p.a .

An agent charges 12% commission on the sales. What does he earn if the total sale amounts to Rs. 36,000? What does the seller get?     

Natarajan and Mr. Gopalan are partners in the company having capitals in the ratio 4 : 5 and the profits received by them are in the ratio 5 :4. If Mr. Gopalan invested capital in the company for 16 months, how long was Mr. Natarajan’s investment in the company?

The present worth of the sum of Rs. 5,830, due 9 months hence, is Rs. 5,500. Find the rate of interest.

A wholesaler allows 25% trade discount and 5% cash discount.  Find the list price of an article, if it was sold for the net amount of Rs 1,140.

A manufacturer can sell x items (x > 0) at a price of Rs.(280 - x) each. The cost of producing x items is Rs. (x² + 40x + 35). Find the number of items to be sold so that the manufacturer can make maximum profit.

The price of a T.V. set is Rs 17,000. An agent charges at 3% and earns Rs. 25,500. Find the number of T.V. sets sold by him. 

If the present worth of a bill due 6 months hence is Rs. 2,500 at 10% per annum, what is the true discount ?