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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 percentag
Question

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?

A.

22%

B.

27.27%

C.

24%

D.

26.32%

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 =  11.12\frac{1}{1.12}​​

Selling 12% light weights

Effective SP per kg = 10.88\frac{1}{0.88}​​

Total gain per kg = 10.8811.12=75308\frac{1}{0.88} -\frac{1}{1.12} = \frac{75}{308} 

Profit% = 75/3081/1.12×100=311×100=27.27%\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 % = (100+b100a×100)100\left(\frac{100+b}{100-a}×100\right)−100​​

Here a =12, b = 12:

Profit % = (100+1210012×100)100\left(\frac{100+12}{100-12}​×100\right)−100

(11288×100)100\left( \frac{112}{88}\times100 \right) - 100  

= 127.27 − 100

= 27.27%

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