Due to decrease in manpower, the production in a factory decreases by 30%. By what per cent should the working hours be increased to restore the original production?

Correct option is B

Given:

The production of factory decreased by 30%

Formula Used:

Successive formula =$$x + y + \frac{xy}{100}$$​​

Solution:

Let the production of factory be 100

Production decreased by 30%

New production = 100 - 30% of 100 = 70

To restore the original production the working hours to be increased by = 100-70 = 30

Percent increase in working hours = $$\frac{30}{70} \times 100 = \frac{300}{7} = 42\frac{6}{7}\%$$​​

Alternative Method:

Using successive formula:

Let increased working hours be x then:

​$$0 = -30 + x + \frac{(-30)x}{100}$$​​

​$$30 = x - 0.3x = 0.7x$$​​

​$$x= \frac{30}{0.7} = 42\frac{6}{7}\%$$​