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Two articles were bought for the same price. One was sold at 40%

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souvonik2k
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Two articles were bought for the same price. One was sold at 40% [#permalink] New post   30 Jan 2018, 11:45
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Two articles were bought for the same price. One was sold at 40% profit and the other was sold at 30% loss. Find the overall percentage of profit/loss made.
A) 5% profit
B) 5% loss
C) 10% profit
D) 10% loss
E) None of these
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A
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Re: Two articles were bought for the same price. One was sold at 40% [#permalink] New post   30 Jan 2018, 12:41
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Cost price be 100x

SP1 = 140x
SP2 = 70x

Total Cost price of two items : 200x
Total Selling price of two items : 210x

Profit/loss = (210x-200x)/200x = 5% profit
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Re: Two articles were bought for the same price. One was sold at 40% [#permalink] New post   30 Jan 2018, 12:00
Choose numbers

100

40% profit = 140
30% loss = 70

70+140-200/200= 10/200

Or 5/100 5 percent profit .




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Re: Two articles were bought for the same price. One was sold at 40% [#permalink] New post   31 Jan 2018, 03:03
souvonik2k wrote:
Two articles were bought for the same price. One was sold at 40% profit and the other was sold at 30% loss. Find the overall percentage of profit/loss made.
A) 5% profit
B) 5% loss
C) 10% profit
D) 10% loss
E) None of these


As \(CP(x)\) = \(CP(y)\) = \(a\).....
\(SP(x) = 1.4a\), \(SP(y) = 0.7a\)
Total \(CP (x & y) = 2a\), Total \(SP (x&y) = 2.1a\)
\(Difference = 0.1a\)
\(% Profit\) = \(\frac{0.1a}{2a}\)
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Re: Two articles were bought for the same price. One was sold at 40% [#permalink] New post   31 Jan 2018, 04:59
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souvonik2k wrote:
Two articles were bought for the same price. One was sold at 40% profit and the other was sold at 30% loss. Find the overall percentage of profit/loss made.
A) 5% profit
B) 5% loss
C) 10% profit
D) 10% loss
E) None of these


Solution



    • Let us assume that the cost price of each article as X.
    • Since the first article was sold at a profit of 40%, we can write –
      o SP1 = (1+40%) of X
      o SP1 = 1.4 X
    • Since the second article was sold at a loss of 30%, we can write –
      o SP2 = (1 – 30%) of X
      o SP2 = 0.7 X
    • Thus, total Selling Price = 1.4X + 0.7X = 2.1 X and
    • Total Cost Price = X + X = 2X
    • Total Profit Percentage = (SP/CP -1) * 100 = 2.1X/2X – 1) * 100 = 5%

Correct Answer : Option A

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Re: Two articles were bought for the same price. One was sold at 40% [#permalink] New post   31 Jan 2018, 11:13
souvonik2k wrote:
Two articles were bought for the same price. One was sold at 40% profit and the other was sold at 30% loss. Find the overall percentage of profit/loss made.
A) 5% profit
B) 5% loss
C) 10% profit
D) 10% loss
E) None of these


Let CP be 100 each, so total CP is 200
SP of one item is 140 & SP of the other item is 70 , Total SP is 210

So, Total Profit is \(\frac{10}{200}*100\) = 5% Profit, Answer will be (A)
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Re: Two articles were bought for the same price. One was sold at 40% [#permalink] New post   02 Feb 2018, 12:05
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souvonik2k wrote:
Two articles were bought for the same price. One was sold at 40% profit and the other was sold at 30% loss. Find the overall percentage of profit/loss made.
A) 5% profit
B) 5% loss
C) 10% profit
D) 10% loss
E) None of these


We can let the cost of each article be c. Thus total cost of the two articles would be 2c. Since one article make a 40% profit or 0.4c profit and the other article made a 30% loss or 0.3c loss. The total profit made is 0.4c + (-0.3c) = 0.1c. Thus the total profit as a percentage of total cost is:

0.1c/2c = 0.1/2 = 1/20 = 0.05 = 5%

Alternate Solution:

Assume that each item costs $100, for a total cost of $200. The first is sold for $140, and the second is sold for $70. Thus, the total revenue is $210, yielding a profit of 210 - 200 = 10. We see that the $10 profit, as a percentage of $200, is 10/200 = 1/20 = .05, or 5%.

Answer: A
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Re: Two articles were bought for the same price. One was sold at 40% [#permalink] New post   20 Aug 2022, 06:46
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Re: Two articles were bought for the same price. One was sold at 40% [#permalink]
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