A faulty weighing machine reads 1 kg when 900 gm is weighted on it. The shopkeeper marked the price of his goods by 10%

A faulty weighing machine reads 1 kg when 900 gm is weighted on it. The shopkeeper marked the price of his goods by 10%, but unfortunately, he was caught by the metrology department and then they ordered him to repair his weighing machine and gave punishment to sell the goods at 10% discount on cost price for a month. If each customer is now paying 220 for 1 kg, then before the raid amount, they have paid for the same quantity.

a) 28.20

b) 27.16

c) 25.25

d) 20.20

Sol:

It is given that initially, weighing machine weighs 900 gm instead of 1000 gm  So, it means shopkeeper earns 100 gm profit on  selling 900 gm goods  

⇒ Profit % = Profit/C.P. × 100  

⇒ Profit% = 100/900 × 100 = 11.11% 

So, he earns this by alteration of weight along with he marked up the price by 10%   Means his overall profit can be calculated by successive  

Overall profit = 11.11 + 10 + (11.11 × 10)/100 = 22.22%  But , now the shopkeeper sells the goods at Rs20 per kg after giving 10% discount  Actual Cost price of 1kg sugar = 100 /(100 – 10) × 20 = 100/90 × 20 = Rs22.22  And earlier shopkeeper was selling at 22,22% profit   So, Selling price = (100 + 22.22) /100 × 22.22   ⇒ 122.22/100 ×22.22 = Rs27.157  ≈ Rs27.16 ( rounded off to two  places of decimals)  Hence, they have paid ₹27.16 for the same quantity .