In USA, Goods and Services Tax (GST), is a tax levied on the sale of all goods and services. In the other countries, it is known as Value Added Tax (VAT). For example, if an item is priced at $100 excluding GST, which is currenly 7%, a customer will pay $100 plus 7% of $100, i.e. $107.

1) The TV set Bala wants to by is on sale in two shops: BEST BUY and BUY& SAVE. 

 If the GST rate is 7%, which shop offers the better price?

2) If a discount of 10% is given to a bill, $128 remains to be paid. How much is the bill? How much is the bill?

If a GST of 7% is included in the bii, how much is the GST?

Calculate sum of angles in star shape:

1) Find the sum of angles A, B, C, D, E in the diagram below.

2) If 2A = B = C = D = E, find A.

Fractions of the form \(\dfrac{1}{n}\), where n is an integer, are known as unit fractions.

1) Express the number 1 as a sum of six different unit fractions, given that four of them are \(\dfrac{1}{2},\dfrac{1}{9},\dfrac{1}{10},\dfrac{1}{18}\).

2) Express the number 1 as a sum of seven different unit fractions, given that five of them are \(\dfrac{1}{3},\dfrac{1}{5},\dfrac{1}{9},\dfrac{1}{15},\dfrac{1}{45}\).

Given a sequence of real numbers \(\left(x_n\right)\left(n=1,2,3,...\right)\)  satisfying the following conditions   \(\left|x_1\right|< 1\) , and  

                                        \(x_{n+1}=\dfrac{-x_n+\sqrt{3-3x^2_n}}{2}\) , for all \(n\ge2\).

What additional condition on \(x_1\) ensures that all numbers of the above sequence are positive?

Let be given positive numbers a, b, c so  that abc = 1. Prove that :

a)  \(\left(\dfrac{1}{1+a}\right)^2+\left(\dfrac{1}{1+b}\right)^2+\left(\dfrac{1}{1+c}\right)^2\ge\dfrac{3}{4}\).

b) \(\left(\dfrac{1}{1+a}\right)^3+\left(\dfrac{1}{1+b}\right)^3+\left(\dfrac{1}{1+c}\right)^3\ge\dfrac{3}{8}\) ,

The digits , , , , and  are each used once to write a five-digit number  \(abcde\) . The three-digit number \(abc\)  is divisible by , the three-digit number \(bcd\)  is divisible by , and the three-digit number \(cde\)  is divisible by . What is \(a\)?