Question 1.10: (a) Calculate (i) 23% of 1534 (ii) 100% of 1534 (b) A salary......

(a) In calculations, quoted percentages are always written as the fraction, quoted percentage/ 100.

(i) 23% of 1534 = \frac{23}{100} \frac{1534}{1} = \frac{(23)(1534)}{100} =  \frac{35 282}{100} = 352.82

(ii) 100% of 1534 = \frac{100}{100}\frac{1534}{1} = \frac{(100)(1534)}{100} = 1534       So, 100% of (anything) = (anything)

(b)  (i) 12% of 55 240 = \frac{12}{100}\frac{55 240}{1} = \frac{12(5524)}{10} = \frac{66 288}{10} = 6628.8 =  increase  So the increase in salary is £6628.8

(ii) The new salary is £55 240 + £6628.8 = £61 868.8

Alternatively, the new salary is 112% of the previous salary and may be calculated as

55 240\times{\bigg(}{\frac{112}{100}}{\bigg)}=£61 868.8

(c) Let the 2007 price be the basic price. The price in 2013 is 60% of the 2007 price, i.e., 2013 price = 60% × basic price.

So £63 400 = 60% of the basic price and we want to find 100% of the basic price.

Method

63 600 = \frac{60}{100} × basic price          60% × basic price

\frac{63 600}{60} = \frac{1}{100} × basic price    find 1% of the basic price

\frac{63 600}{60} × \frac{1}{100} = \frac{100}{100} × basic price    100% of the basic price

106 000 = basic price

So, in 2007, the apartment cost £106 000.