Due to reduction in workforce, the production in a factory decreases by 30%. By what percentage should the working hours per person be increased to restore the original production? (Correct to two decimal places.)

As we know that the production in a factory = number of people working $$\times$$ time.

So when 30% production decreased, then 30% work force will also be decreased.

Let's assume that initially 'y' people were working in the factory and each of them is working 'z' hours.

initially production = yz

Let's assume the percentage increase in the working hours per person to restore the original production is 'p'.

yz = y of (100-30)% $$\times$$ z of (100+p)%

yz = y of 70% $$\times$$ z of (100+p)%

$$1=\frac{70}{100}\times\frac{(100+p)}{100}$$

$$1=\frac{7}{1000}\times(100+p)$$

$$100+p = \frac{1000}{7}$$

$$p = \frac{1000}{7} - 100$$

$$p = \frac{1000-700}{7}$$

$$p = \frac{300}{7}$$

p = 42.86% (approx.)