A businessman cheats by using faulty weights, to the tune of 12% each time, when buying and selling material. What is the rise in his profit percentage using faulty weights only?

Correct option is B

Given:

Cheating with faulty weights of 12% while buying and 12% while selling.

Solution:

​Let CP = ₹1 per kg (standard), SP = ₹1 per kg (standard) initially without cheating.

With false weights:

Buying 12% heavy weights 

Effective CP per kg =  $$\frac{1}{1.12}$$​​

Selling 12% light weights

Effective SP per kg = $$\frac{1}{0.88}$$​​

Total gain per kg = $$\frac{1}{0.88} -\frac{1}{1.12} = \frac{75}{308}$$ 

Profit% = $$\frac{75/308}{1/1.12} \times 100 = \frac3{11}\times 100 = 27.27\%$$​​

Alternate Solution: ​

If he cheats by a% in buying and b% in selling,

Profit % = $$\left(\frac{100-a}{100+b}×100\right)−100$$​​

Here a =12, b = 12:

Profit % = $$\left(\frac{100−12}{100+12}​×100\right)−100$$

= $$\left( \frac{88}{112}\times100 \right) - 100$$ 

= 127.27 − 100

= 27.27%