Harris has two weights of one kilogram at his shop. One of the weights is accurate while the other actually weighs 1100 grams. While measuring the goods, he uses one of the two weights. The probability that he uses a wrong weight is 3/5. If he sells the goods at the cost price, how much profit or loss will he make?
Solution
Correct Answer: Option B
When Harris picks the wrong weight, he weighs 1100 grams but takes price of 1000 grams only. This is true in 3 cases out of 5. In remaining two cases, he weighs with accurate weight.
⇒ In 5 cases, quantity he weighs = (3 × 1100) + (2 × 1000) = 5300 grams
In 5 cases, quantity for which he takes price = (5 × 1000) = 5000 grams
He sells goods at cost price.
Suppose cost price of 1 gram is T.
⇒ On selling 5300 grams, cost price for Harris = 5300T
Selling price = Cost price of 5000 grams = 5000T
We know, Selling Price = Cost Price × (1 - (Loss %)/100)
⇒ 5000T = 5300T × (1 - (Loss %)/100)
⇒ Loss percentage \(= {\rm{\;}}100{\rm{\;}} \times {\rm{\;}}\left( {1{\rm{\;}} - \frac{{5000{\rm{T}}}}{{5300{\rm{T}}}}} \right){\rm{\;}} = {\rm{\;}}5.66\)
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