Higher June 2018 Paper 1 Q11
11.
(a) The costs of building a single-storey house extension are in the ratio
labour : materials : professional fees = 7 : 5 : 1.
The cost of materials is £6400 more than the amount paid in professional fees.
Work out the total cost of building this house extension. [4]
(b) Ten years ago, the costs of converting a loft to a bedroom were £7200 for labour, £6000 for materials and £1200 for professional fees.
Today, the same loft conversion would cost a total of £30 800.
- Labour costs are \(1\tfrac{2}{3}\) times as much.
- Materials costs have increased by 150%.
Show that the amount paid in professional fees is just over 3 times as much. [4]
| Scheme | Marks | Comments |
|---|---|---|
| 4 parts = (£)6400 or 6400 ÷ 4 or \(5x - x =\) 6400 or equivalent | M1 | Accept \(\dfrac{4}{13}\) is 6400 or equivalent |
| (1 part = £) 1600 | A1 | |
| (Total cost = £) 1600 × 13 or (Total cost = £) 11200 + 8000 + 1600 | m1 | for ‘their 1600’ × 7 + ‘their 1600’ × 5 + ‘their 1600’ or for ‘their 1600’ × 13 or for sight of 9600 or 8000 |
| = (£) 20800 | A1 | CAO If no marks, award SC2 for an answer of (£)16640 or SC1 for sight of 6400 × 13 ÷ 5 or equivalent |
| Scheme | Marks | Comments |
|---|---|---|
| (labour = ) \(7200\times\dfrac{5}{3}\) (= 12000) | M1 | Or equivalent full method. |
| (materials =) 6000 × 2.5 (= 15000) | M1 | Or equivalent full method. |
| (professional fees =) \(30800 - 7200\times\dfrac{5}{3} - 6000\times2.5\) (= 30800 – 12000 – 15000) | M1 | FT ‘their \(7200\times\dfrac{5}{3}\)’ and ‘their 6000 × 2.5’ provided one is correct. |
| (professional fees =) 3800 (which is just over 3 × 1200) | A1 | CAO |
| (8) |