Solve the following mathematical problems:

• (a) Amin has 12 pieces of Tk. 10 and Tk. 5 notes in his wallet. If the total value of all the notes less than Tk. 95, what is the maximum number of Tk. 10 notes that he has?

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  921

• (b) A, B and C enter into partnership. A invests 3 times as much as B invests and B invests two-third what C invests. At the end of the year, the profit earned is Tk. 6,600. What is the share of B?

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  225

• (c) A and B can complete a work in 15 days and 10 days respectively. They started doing the was together but after 2 days B had to leave and A alone completed the remaining work. H many days did it took to complete the whole work?

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  293

• (d) A depositor deposited Tk. 4,000 as x% simple interest and Tk. 5,000 at y % simple interest. received annual interest of Tk. 320 on his deposited amounts at the year end. If he could deposit Tk. 5,000 at x% simple interest and Tk. 4,000 at y% simple interest, he would recce annual interest of Tk. 310. Find the value of x and y.

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  314

• (e) 70 students are studying physics, mathematics and chemistry. 40 students study mathematics, 35 students study physics and 30 students study chemistry 15 students are studying all the subjects. How many students are studying exactly two of the subject?

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  664

• (f) Find the value of  $x^6+\frac{1}{x^6},$ if $x+\frac{1}{x}=3$

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  236

• (g) solve the equation: $\frac{3}{x+2}+\frac{x+1}{x-5}=2$

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  269