1. **Problem statement:** A number increases by 40% and then decreases by $a$%, resulting in an overall percentage change of -2%. We need to find the value of $a$. 2. **Formula used:** When a quantity changes by $x$% and then by $y$%, the overall change is given by: $$\text{Overall change} = (1 + \frac{x}{100})(1 + \frac{y}{100}) - 1$$ 3. **Apply the given values:** Here, the first change is an increase of 40%, so $x = 40$. The second change is a decrease of $a$%, so $y = -a$. The overall change is -2%, so: $$ (1 + \frac{40}{100})(1 + \frac{-a}{100}) - 1 = \frac{-2}{100} $$ 4. **Simplify the equation:** $$ (1 + 0.4)(1 - \frac{a}{100}) - 1 = -0.02 $$ $$ 1.4 \left(1 - \frac{a}{100}\right) - 1 = -0.02 $$ 5. **Expand and simplify:** $$ 1.4 - 1.4 \times \frac{a}{100} - 1 = -0.02 $$ $$ 0.4 - \frac{1.4a}{100} = -0.02 $$ 6. **Isolate $a$:** $$ - \frac{1.4a}{100} = -0.02 - 0.4 $$ $$ - \frac{1.4a}{100} = -0.42 $$ 7. **Multiply both sides by -100:** $$ 1.4a = 42 $$ 8. **Solve for $a$:** $$ a = \frac{42}{1.4} = 30 $$ **Final answer:** The value of $a$ is 30%.