To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present?

### Concept & Formula This problem is governed by the principle of Inverse Proportion. When the total volume required to fill a container remains constant, the number of buckets needed is inversely proportional to the capacity of each bucket. $$ \text{Total Volume} = \text{Number of Buckets} \times \text{Capacity per Bucket} $$ $$ N_1 \times C_1 = N_2 \times C_2 $$ ### Step-by-Step Solution * **Given:** Initial number of buckets ($N_1$) = 25 Let initial bucket capacity be $C_1 = x$. New bucket capacity ($C_2$) = $\frac{2}{5}$ of present = $\frac{2}{5}x$. * **Calculation:** Establish the total capacity of the tank using the initial conditions: $$ \text{Tank Volume} = 25 \times x = 25x $$ * Set up the equation for the new conditions to find the new number of buckets ($N_2$): $$ N_2 \times \left(\frac{2}{5}x\right) = 25x $$ * Solve for $N_2$ by dividing both sides by $x$ and multiplying by the reciprocal of $\frac{2}{5}$: $$ N_2 = \frac{25x}{\frac{2}{5}x} $$ $$ N_2 = 25 \times \frac{5}{2} $$ $$ N_2 = \frac{125}{2} $$ $$ N_2 = 62.5 \text{ or } 62\frac{1}{2} $$ ### Exam Strategy & Shortcut Use the **Fractional Inverse Shortcut**. If the capacity of a tool becomes a certain fraction ($\frac{a}{b}$) of its original size, the number of tools required to do the identical job becomes the reciprocal fraction ($\frac{b}{a}$) of the original number. Here, capacity becomes $\frac{2}{5}$. Therefore, the number of buckets needed becomes $\frac{5}{2}$ times the original amount. $$ 25 \times \frac{5}{2} = 62.5 $$ This mental math maneuver allows you to solve the problem in seconds. ### Common Pitfall A standard error is directly multiplying the original number of buckets by the new capacity fraction ($25 \times \frac{2}{5} = 10$). This mistakenly assumes direct proportionality. Remember: smaller buckets mean *more* buckets are required, not fewer. ### Final Answer Therefore, the correct answer is **$62\frac{1}{2}$**.