Alliance Form 3 P1 Q18 — Area, Tiles & Profit

KCSE (Form 3) Form 3 Measurement

Published

The Question

“A floor measuring 10 and a half metres by 6 metres is to be covered with square tiles of side 30 cm. First find the number of tiles needed to cover one floor. Then find the cost of the tiles required for 15 such rooms if the tiles are sold in cartons of 20 at 800 shillings per carton. Finally, if the dealer also spends 2,000 shillings on transport and 600 shillings on subsistence, find the selling price per carton that gives a profit of 12 and a half percent.”

1

Convert to centimetres and find the floor area

The tile size is given in centimetres, so change every length to centimetres before working out area. This keeps the units matching, which avoids mistakes. The floor is 10 and a half metres by 6 metres, which becomes 1,050 cm by 600 cm, and multiplying the two sides gives the floor area.

1012 m=1050 cm,6 m=600 cm10\tfrac{1}{2}\,\text{m} = 1050\ \text{cm}, \qquad 6\,\text{m} = 600\ \text{cm}
Floor area=1050×600=630 000 cm2\text{Floor area} = 1050 \times 600 = 630\,000\ \text{cm}^{2}
2

Find the number of tiles for one floor

Each tile is a 30 cm square, so its area is 30 times 30. The number of tiles is simply the floor area shared out into tile-sized pieces, so divide the floor area by the area of one tile.

Area of one tile=30×30=900 cm2\text{Area of one tile} = 30 \times 30 = 900\ \text{cm}^{2}
Number of tiles=630 000900=700\text{Number of tiles} = \frac{630\,000}{900} = 700
3

Cost the tiles for 15 rooms

Fifteen identical rooms each need 700 tiles, so multiply to get the total tiles. Because tiles are only sold in cartons of 20, divide the total by 20 to get the number of cartons, then multiply the cartons by the price of 800 shillings each.

700×15=10 500 tiles700 \times 15 = 10\,500\ \text{tiles}
Cartons=10 50020=525\text{Cartons} = \frac{10\,500}{20} = 525
Cost of tiles=525×800=420 000 shillings\text{Cost of tiles} = 525 \times 800 = 420\,000\ \text{shillings}
4

Add the extra expenses to get total cost

The dealer's real outlay is more than just the tiles: transport and subsistence must be added because they are part of what it cost to bring the tiles to sale. Add 2,000 and 600 shillings to the tile cost.

Extra=2000+600=2600 shillings\text{Extra} = 2000 + 600 = 2600\ \text{shillings}
Total cost=420 000+2600=422 600 shillings\text{Total cost} = 420\,000 + 2600 = 422\,600\ \text{shillings}
5

Add 12.5% profit and split over the cartons

A profit of 12 and a half percent means the selling total is the cost plus one-eighth of the cost, which is the same as multiplying by 1.125. Once you have the total selling price, divide it by the 525 cartons to get the price of a single carton.

Selling total=422 600×1.125=475 425 shillings\text{Selling total} = 422\,600 \times 1.125 = 475\,425\ \text{shillings}
Price per carton=475 425525≈906 shillings\text{Price per carton} = \frac{475\,425}{525} \approx 906\ \text{shillings}

Final Result

One floor needs 700 tiles. The tiles for 15 rooms cost 420,000 shillings. To make a 12.5% profit after transport and subsistence, each carton should be sold for about 906 shillings.

Why this method works

The whole question works because area is measured in equal square units. When both the floor and the tile are expressed in the same unit, dividing the floor area by one tile's area literally counts how many tiles fit, with no gaps or overlaps. The costing then follows real business logic: you can only buy whole cartons, so tiles are grouped in twenties; profit is calculated on the true total cost, which must include transport and subsistence, not just the tiles; and multiplying by 1.125 raises the price by exactly one-eighth, the meaning of 12 and a half percent.

✓

Reverse it: 906 times 525 is about 475,650, and 422,600 times 0.125 is 52,825, so cost plus profit is roughly 475,425 — matching the selling total, confirming the answer.