A number is first decreased by 40% and then increased by 40%. The equivalent change is :

1. nothing

2. 16% increase

3. 16% decrease

4. 8% increase

Let the original number be 100.

After a decrease of 40%, it becomes = 100 - 40% of 100

= $100 - \dfrac{40}{100} \times 100$

= $100 - \dfrac{4000}{100}$

= $100 - 40$

= 60

Now it is increased by 40%, it becomes = 60 + 40% of 60

= $60 + \dfrac{40}{100} \times 60$

= $60 + \dfrac{2,400}{100}$

= $60 + 24$

= 84

∴ Change on the whole = Final value - Initial value

= 84 - 100

= -16

Change on the whole is negative means change on the whole the number is decreasing.

∴ Percentage change = $\dfrac{\text{Change on the whole}}{\text{Initial value}} \times 100$ %

= $\dfrac{16}{100} \times 100$ %

= 16%

Hence, option 3 is the correct option.