Percentage problem 2

Let the man's wage be $100$ rupees.

If it is decreased by 50% , then it becomes $100-(100*\dfrac{50}{100})=50$ rupees.

Now, if it is increased again,then it becomes $75.$ (How ?)

Therefore net loss is $\dfrac{100-75}{100}=25$ %

If $w$ represents the man's wages, then the man earns $(1-0.5)w=0.5w=w_0$ after the first alteration in his income. After the second, he earns $(1+0.5)w_0=\frac{3}{2}\cdot\left(\frac{1}{2} w\right)=\frac{3}{4}w=0.75w.$ Since the problem asks us what the net loss of his wages are, we just calculate $1-0.75=0.25$ , i.e., a $25\%$ loss in wages.

Suppose man's wages is 100
if 50% decreases then wages become 100 - 100 * 50/100 = 50
Now wages increased by 50% then it is = 50 + 50 *50/100 = 25
now income become = 50 +25 = 75
loss = 100- 75 = 25
25 of 100 is 25%
there for loss is 25% (Ans.)