A courtyard is 25m long and 16m broad is to be paved with bricks of dimensions 20cm by 10cm. What is the total number of bricks required?

### Concept & Unit Conversion and Area The number of bricks required to pave an area is calculated by dividing the total area to be paved by the surface area of a single brick. Crucially, all dimensions must be in the same units (either all meters or all centimeters). $$Number\ of\ Bricks = \frac{Total\ Area}{Area\ of\ One\ Brick}$$ ### Step-by-Step Solution * Given: Courtyard dimensions are 25 m by 16 m. Brick dimensions are 20 cm by 10 cm. * Convert courtyard dimensions to centimeters (1 m = 100 cm). * Length = $25 \times 100 = 2500$ cm. * Breadth = $16 \times 100 = 1600$ cm. * Calculate the total area of the courtyard: $Area = 2500 \times 1600 = 4,000,000$ cm$^2$. * Calculate the area of a single brick: $Area = 20 \times 10 = 200$ cm$^2$. * Calculate total bricks: Number of bricks = $\frac{4,000,000}{200}$. * Divide to find the result: $\frac{40,000}{2} = 20000$. * A total of 20000 bricks are required. ### Exam Strategy & Shortcut You can set up the calculation as a single fraction and cancel zeroes before multiplying to avoid dealing with massive numbers: $\frac{2500 \times 1600}{20 \times 10} = \frac{250 \times 160}{2 \times 1} = 250 \times 80 = 20000$. ### Common Pitfall Failing to convert the meters into centimeters before calculating the area. If you simply calculate $\frac{25 \times 16}{20 \times 10}$, you will get 2, which is completely incorrect by a magnitude of $10,000$ (since 1 m$^2$ = $10,000$ cm$^2$). ### Final Answer Therefore, the correct answer is **20000**.