12 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?

### Concept & Constant Volume The total volume of the tank remains constant regardless of the size of the bucket used to fill it. We equate the total volume calculated with the first bucket size to the total volume calculated with the second bucket size. $$ N_1 \times V_1 = N_2 \times V_2 $$ ### Step-by-Step Solution 1. **Calculate Total Capacity:** * Volume of one large bucket = 13.5 litres. * Number of large buckets used = 12. * Total capacity of the tank = $12 \times 13.5$ litres. 2. **Calculate Number of Smaller Buckets:** * Volume of one small bucket = 9 litres. * Let the number of small buckets needed be $x$. * $x \times 9 = 12 \times 13.5$ 3. **Solve for $x$:** * $x = \frac{12 \times 13.5}{9}$ * Simplify the fraction: $\frac{12}{9} = \frac{4}{3}$. * $x = \frac{4}{3} \times 13.5 = 4 \times 4.5$ * $x = 18$ ### Exam Strategy & Shortcut Use inverse proportionality. The capacity of the bucket dropped from 13.5 to 9. Ratio of bucket capacities = $13.5 : 9 = 135 : 90 = 3 : 2$. Since capacity and number of buckets are inversely proportional, the ratio of the number of buckets will be $2 : 3$. If 2 parts = 12 buckets, then 1 part = 6 buckets. So, 3 parts = $3 \times 6 = 18$ buckets. ### Common Pitfall Performing the full multiplication ($12 \times 13.5 = 162$) before dividing wastes time. Always keep the numbers in a fraction and cancel out common terms first. ### Final Answer Therefore, the correct answer is **18**.