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### Show Tags

26 Oct 2018, 19:14
4
00:00

Difficulty:

45% (medium)

Question Stats:

70% (03:02) correct 30% (02:26) wrong based on 27 sessions

### HideShow timer Statistics

If John purchased goods for $1050, and sold $$\frac{1}{3}$$rd of these goods at a loss of 12%, then at what gain percent should remainder goods be sold to gain 18% on the whole transaction? A. 31% B. 33% C. 43% D. 67% E. 77% _________________ ____________________________ Regards, Chaitanya +1 Kudos if you like my explanation!!! Manager Joined: 14 Jun 2018 Posts: 188 If John purchased goods for$1050  [#permalink]

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26 Oct 2018, 23:42
1
Using alligation ,
$$\frac{x-18}{18-(-12)} = \frac{1}{2}$$
2x - 36 = 30
x = 33

Can be done with weighted average formula as well

or the classic

$$350 * \frac{88}{100} + 700 \frac{(100+k)}{100} = 1050 * \frac{118}{100}$$
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Re: If John purchased goods for $1050 [#permalink] ### Show Tags 27 Oct 2018, 02:14 1 eswarchethu135 wrote: If John purchased goods for$1050, and sold $$\frac{1}{3}$$rd of these goods at a loss of 12%, then at what gain percent should remainder goods be sold to gain 18% on the whole transaction?

A. 31%
B. 33%
C. 43%
D. 67%
E. 77%

Given: John sells 1/3rd of the overall stock at a loss of 12%

We are asked to find at which gain must he sell the remaining 2/3rd of the stock

Let's call that margin - x%. Since the ratio at which the stock is sold is 1:2,
we can deduce the following equatation -> $$1*0.88 + 2*x = 3*1.18$$

Simplifying that further, we get $$2x = 3.54 - 0.88 = 2.66$$ -> $$x = \frac{2.66}{2} = 1.33$$

Therefore, the remaining goods are sold at 33%(Option B) more to realize the 18% overall profit margin.
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