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17 Nov 2020, 02:45
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D
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Difficulty:
75%
(hard)
Question Stats:
64% (03:01) correct
36%
(03:00)
wrong
based on 214
sessions
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Ramesh sells one-third of his goods at a profit of 20%. One-third of the remaining goods get damaged and have to sold at a loss of 10%. At what minimum profit percentage should the rest of the goods be sold such that Ramesh makes an overall profit of atleast 10%?
A. 16.25%
B. 15%
C. 14.28%
D. 12.5%
E. 10 %
A. 16.25%
B. 15%
C. 14.28%
D. 12.5%
E. 10 %
15 Dec 2020, 04:30
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nityakaul02
There is a nice short cut for these type of sums. Only thing we must remember is to take the loss percentage as negative.
1/3 rd of the goods was sold at 10% profit and 1/3 of the remaning 2/3 = 2/9 th of the goods was sold at a loss of 10%.
To get an overall profit of 10% at what profit % should the remaining 1 - 1/3 - 2/9 = 4/9 th of the goods be sold.
Let the required profit % = x
So \(\frac{1}{3}*20 + \frac{2}{9} * (-10) + \frac{4}{9} * x = 10\) (overall profit)
\(\frac{60 - 20 + 4x}{9} = 10\)
40 + 4x = 90
4x = 50
x = 12.5%
Option D
Arun Kumar
General Discussion
17 Nov 2020, 06:24
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Consider a total of 9 goods with each 100rs.
i.e. for the 1/3 of 9 goods sold at 20% profit
=> 3 goods of 100rs each sold at 20% profit => the final amount he has after selling 3 goods is 360rs.
Now he sells 1/3 of remaining goods i.e. 1/3 of 9 goods sold at 10% loss
=> 2 goods sold at 10% loss => the final amount he has after selling 2 goods is 180rs.
As per the question, the final amount that he should have at least a 10% profit
=> 9 goods sold at 10% profit => the final amount he will have after selling 9 goods is 990rs.
But we have already sold 5 goods for rs(360+180) i.e. 5 goods sold for 540rs.
Remaining 4 goods should be sold at 450 rs.
=> (450-cost price of 4 goods)/cost price of 4 goods
=> (450-400)/400
=> 12.5% profit
Therefore he should sell the remaining goods at '12.5%' profit to have a 10% profit on total.
i.e. for the 1/3 of 9 goods sold at 20% profit
=> 3 goods of 100rs each sold at 20% profit => the final amount he has after selling 3 goods is 360rs.
Now he sells 1/3 of remaining goods i.e. 1/3 of 9 goods sold at 10% loss
=> 2 goods sold at 10% loss => the final amount he has after selling 2 goods is 180rs.
As per the question, the final amount that he should have at least a 10% profit
=> 9 goods sold at 10% profit => the final amount he will have after selling 9 goods is 990rs.
But we have already sold 5 goods for rs(360+180) i.e. 5 goods sold for 540rs.
Remaining 4 goods should be sold at 450 rs.
=> (450-cost price of 4 goods)/cost price of 4 goods
=> (450-400)/400
=> 12.5% profit
Therefore he should sell the remaining goods at '12.5%' profit to have a 10% profit on total.
