Question

Hansi and Megan go on holiday. The costs of their holidays are in the ratio
Hansi : Megan = 7 : 4.
Hansi’s holiday costs $756. Find the cost of Megan’s holiday. [2]
(b) In 2008, Hansi earned $7800.
(i) He earned 15% more in 2009. Calculate how much he earned in 2009. [2]
Hint : Calculate 15% of 7800. Add this value to $7800
(ii) In 2010, he earns 10% more than in 2009.Calculate the percentage increase
in his earnings from 2008 to 2010. [3]
(c) Megan earned $9720 in 2009. This was 20% more than she earned in 2008.
How much did she earn in 2008? [3]
(d) Hansi invested $500 at a rate of 4% per year compound interest. Calculate
the final amount he had after three years. [3]

Answer 1

Given :

a) The cost of holiday is in ratio , Hansi : Megan = 7 : 4

Hansi's holiday cost = $756

b)Earning of Hansi in 2008 = $7800

Earning in 2009 = 15% more than in 2008

Earning in 2010 = 10% more than in 2009

c) Earning of Megan in 2009 = $9720

This was 20% more than she earned in 2008

d) P = $500

R = 4%

T = 3years

To find :

a) Cost of Megan's holiday.

b) Earning in 2009

Percentage increase  in his earnings from 2008 to 2010

c) Earning in 2008

d)  Final amount after three years

Solution :

a) Let cost of Megan's holiday = x

7 : 4 = 756 : x

x = 756 × 4 / 7

x = $432

Megan's holiday costs $432.

b) i) Earning in 2009 = 7800 + (7800 × 15 / 100)

Earning in 2009 = 7800 + 1170

Earning in 2009 = $8970

He earned $8970 in year 2009.

ii) Earning in 2010 = 8970 + (8970 × 10 / 100)

Earning in 2010 = 9867

Percentage increased = (9867 - 7800) × 100 / 7800

Percentage increased = 26.5%

Percentage increase in Hansi's earning from  2008 to 2010 is 26.5%.

c) Let Megan's earning in 2008 = x

9720 = x + (x × 20 / 100)

9720 = x + x / 5

9720 = 6x / 5

x = 9720 × 5 / 6

x = $8100

Megan's earning in 2008 is $8100.

d) $A = P(1 + \frac{R}{100} )^{T}$

$A = 500(1 + \frac{4}{100} )^{3}$

$A = 500(1+\frac{1}{25} )^{3}$

$A = 500(\frac{26}{25}) ^{3}$

A = $562.43

Final amount after three years is $562.43.