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| A LPP Puzzle (Posted on 2006-12-11) |
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Long ago, in Medieval Europe, there lived an unscrupulous trader named Escrocfleuve. One day he decided to utilise one of his false balances both in buying and selling of Item A, thereby gaining 11.44% more than the LPP on the item. It was noted that if the scale pans on which Item A was weighed were interchanged, Escrocfleuve's actual percentage profit would have been 10.4% less than the LPP on the said item. Determine the LPP on Item A in that transaction.
On another occasion, Escrocfleuve used another of his defective balances on the buying and selling of Item B. This time he gained 9.9% more than the LPP on the item. It was noted that if the scale pans on which Item B was weighed were interchanged, Escrocfleuve would still achieve an overall profit of 2.01% by the transaction. Determine the LPP on Item B in the other transaction.
Note: Legitimate Percentage Profit (LPP) is the profit achieved by a person in the buying and selling of an article with a true balance; assume, for the current problem, that LPP is always positive.
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Submitted by K Sengupta
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Rating: 3.0000 (2 votes)
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Solution:
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PART A:
Let M and N denote the apparent weights of Item A when bought and sold respectively.
Let p denote the Prime Cost per unit weight of the article, while x denotes the Legitimate Percentage Profit on the article.
Accordingly:
(i) N*p*( 1 + x/100) = M*p*[1 + (x+11.44)/100] ;
(ii) M*p*(1 + x/100) = N*p*[1 + (x-10.4)/100]
From (i) and (ii); we obtain:
(1 + x/100)^2 = [1 + (x+11.44)/100]* [1 + (x-10.4)/100]
Or, (111.44 + x)(89.6 + x) = (100 + x)^2
Or, 1.04x = 14.976 ( Upon simplification)
Or, x = 14.4
Hence, the required LPP on Item A was 14.4 percent.
PART B
Let M and N denote the apparent weights of Item B when bought and sold respectively.
Let p denote the Prime Cost per unit weight of the article, while x denotes the Legitimate Percentage Profit on the article.
Accordingly:
(i) N*p*( 1 + x/100) = M*p*[1 + (x + 9.9)/100] ;
(ii) M*p*(1 + x/100) = N*p*[1 + 2.01/100]
From (i) and (ii); we obtain:
(100 + x)^2 = (109.9 + x)(102.01)
Or, x^2 + 97.99x – 1210.899 = 0
Or, (x + 109.09)(x – 11.1) = 0
Or, x = 11.1 ( ignoring the negative value which is inadmissible)
Hence, the required LPP on Item B was 11.1 percent.
*** Also, refer to the solutions to Parts A and B provided by Charlie in the comment section.
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