Discussion
How many planks of size 2 m × 35 cm × 8 cm can be made from a wooden block 8 m long, 70 cm wide and 40 cm thick ?
Answer: B
40 planks can be made.
Put all lengths in centimetres. The block is 800 cm × 70 cm × 40 cm and each plank is 200 cm × 35 cm × 8 cm.
\[ \begin{aligned} \text{planks} &= \frac{800 \times 70 \times 40}{200 \times 35 \times 8} \\ &= \frac{2240000}{56000} = 40 \end{aligned} \]
The dimensions also fit exactly: 800/200 = 4 along the length, 70/35 = 2 across the width and 40/8 = 5 through the thickness, and 4 × 2 × 5 = 40, so no wood is wasted.
Forgetting to convert metres to centimetres is the usual source of the other answers.
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