Question

A dishonest shopkeeper pretends to sell his goods at cost price but uses false weights and gains $ 11\dfrac{1}{9}\% $ . For weight of 1 kg he uses
A. a weight of 875 grams
B. a weight of 900 grams
C. a weight of 950 grams
D. a weight of 850 grams

Answer 1

Hint: We are given that the shopkeeper sells his goods using false weights. The profit percentage is $ 11\dfrac{1}{9}\% $ . Find the cost weight when its selling weight is 1kg using the below formula.
Formulas used:
 $ Profit = \dfrac{{\left( {SP - CP} \right)}}{{CP}} \times 100 $ , where SP is the selling weight and CP is the cost weight.

Complete step-by-step answer:
We are given that A dishonest shopkeeper pretends to sell his goods at cost price but uses false weights and gains $ 11\dfrac{1}{9}\% $ .
We have to find the true weight he used for 1 kg.
One kilogram is equal to 1000 grams.
The weight 1 kg is the selling weight we need to find its cost weight.
Profit is given in a mixed fraction; convert it into a regular fraction. Profit he gains is $ 11\dfrac{1}{9}\% = \dfrac{{100}}{9}\% $
 $ Profit = \dfrac{{\left( {SP - CP} \right)}}{{CP}} \times 100 $
Substituting the values of profit and selling weight, we get
 $
  SP = 1000grams,Profit = \dfrac{{100}}{9}\% \\
   \Rightarrow Profit = \dfrac{{\left( {SP - CP} \right)}}{{CP}} \times 100 \\
   \Rightarrow \dfrac{{100}}{9} = \dfrac{{1000 - CP}}{{CP}} \times 100 \\
   \Rightarrow \dfrac{{1000 - CP}}{{CP}} = \dfrac{{100}}{{9 \times 100}} = \dfrac{1}{9} \\
   \Rightarrow 9\left( {1000 - CP} \right) = CP \\
   \Rightarrow 9000 - 9CP = CP \\
   \Rightarrow 9CP + CP = 9000 \\
   \Rightarrow 10CP = 9000 \\
   \Rightarrow CP = \dfrac{{9000}}{{10}} \\
  \therefore CP = 900grams \\
  $
He used 900 grams for a weight of 1kg. He pretends to sell goods of 900 grams weight as goods of 1 kg.

So, the correct answer is “Option B”.


Note: Here, cost weight is the real weight (true weight) and selling weight is the false weight in which the shopkeeper pretends it as true. To convert a mixed fraction $ x\dfrac{a}{b} $ into normal fraction, multiply x with b and add a to the product $ xb + a $ ; now this result will the numerator of the new fraction and the denominator is same as the mixed fraction, the new fraction is $ \dfrac{{xb + a}}{b} $