A tank is $\frac{2}{5}$ full. If 16 litres of water is added to the tank, it becomes $\frac{6}{7}$ full. The capacity of the tank is

### Concept & Formula This problem tests the application of linear equations to solve fraction-based word problems. The core insight is that the mathematical difference between the two fractions of the tank's capacity corresponds exactly to the physical volume of water added. Let the total capacity of the tank be represented by $x$. ### Step-by-Step Solution * **Given:** Initial volume = $\frac{2}{5}x$ Final volume = $\frac{6}{7}x$ Volume added = 16 litres. * **Calculation:** Set up the equation based on the change in volume: $$ \frac{6}{7}x - \frac{2}{5}x = 16 $$ * Find a common denominator for 7 and 5, which is 35, to subtract the fractions: $$ \frac{30x}{35} - \frac{14x}{35} = 16 $$ $$ \frac{16x}{35} = 16 $$ * Solve for $x$ by multiplying both sides by $\frac{35}{16}$: $$ x = 16 \times \frac{35}{16} $$ $$ x = 35 $$ ### Exam Strategy & Shortcut Use the **LCM & Divisibility Method**. The total capacity must be a value that interacts cleanly with the denominators given in the problem (5 and 7) to yield whole numbers. The Least Common Multiple (LCM) of 5 and 7 is 35. Looking at the options (28, 32, 35, 42), only 35 is perfectly divisible by 5. You can immediately identify 35 as the highly probable correct answer without doing the full algebra, saving precious seconds. ### Common Pitfall A frequent mistake is setting up the equation backwards (subtracting the larger fraction from the smaller one) resulting in a negative capacity. Always double-check which fraction represents the "more full" state to ensure your resulting difference is positive. ### Final Answer Therefore, the correct answer is **35 litres**.