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By selling 12 toffees for a dollar, a shopkeeper loses 20%

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TheNightKing
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By selling 12 toffees for a dollar, a shopkeeper loses 20% [#permalink] New post   11 Feb 2020, 10:37
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By selling 12 toffees for a dollar, a shopkeeper loses 20%. In order to gain 20% in the transaction, he should sell the toffees at the rate of how many toffees for a dollar?
(a) 8
(b) 6
(c) 4
(d) 3
(e) 10
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A
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Re: By selling 12 toffees for a dollar, a shopkeeper loses 20% [#permalink] New post   11 Feb 2020, 13:36
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By selling 12 toffees for a dollar, a shopkeeper loses 20%. In order to gain 20% in the transaction, he should sell the toffees at the rate of how many toffees for a dollar?
(a) 8
(b) 6
(c) 4
(d) 3
(e) 10

Buying Price = x

For 12 toffees :-
Buying Price = 12x
Selling Price = 1

\(Loss = Buying Price - Selling Price => 12x - 1 = 20%(Buying Price) = \frac{12x}{5}\)

\(12x*(\frac{4}{5})=1 => 12x = 5/4 = 1.25\)

To gain 20% he would have to sell 12 toffees at 1.5 $
1.2 B.P = S.P => 1.2*1.25 => 1.5$

If he sells 12 toffees at 1.5, how many would he sell for 1 $

\(= \frac{12}{1.5} = 8\) -> Answer - A
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Re: By selling 12 toffees for a dollar, a shopkeeper loses 20% [#permalink] New post   12 Feb 2020, 08:58
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TheNightKing wrote:
By selling 12 toffees for a dollar, a shopkeeper loses 20%. In order to gain 20% in the transaction, he should sell the toffees at the rate of how many toffees for a dollar?
(a) 8
(b) 6
(c) 4
(d) 3
(e) 10


Please refer to my attachement. I hope it is clear guys ! :
Attachments

toffee.JPG
toffee.JPG [ 93.28 KiB | Viewed 3300 times ]

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Re: By selling 12 toffees for a dollar, a shopkeeper loses 20% [#permalink] New post   17 Feb 2020, 04:16
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TheNightKing wrote:
By selling 12 toffees for a dollar, a shopkeeper loses 20%. In order to gain 20% in the transaction, he should sell the toffees at the rate of how many toffees for a dollar?
(a) 8
(b) 6
(c) 4
(d) 3
(e) 10


We can let C = the cost of the 12 toffees and R = the revenue from the sale of the 12 toffees. We can create the equation:

Profit = -0.2C

R - C = -0.2C

R = 0.8C

1 = 0.8C

1/0.8 = C

1.25 = C

Thus, 12 toffees cost $1.25. In order to make a 20% profit on 12 toffees, the sale price should be 1.25 * 1.2 = $1.50. Then, if 12/1.5 = 8 toffees are sold for $1, a profit of 20% will be realized.

Answer: A
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Re: By selling 12 toffees for a dollar, a shopkeeper loses 20% [#permalink] New post   03 Oct 2021, 04:58
Simply, When 12 toffe sold for 1 doller shopkeeper loses 20%. So this price is actually 80%.
We have to make it 120%

Therefore, \(\frac{12*(100-20)}{(100+20)}\)
\(= \)\(\frac{12*80}{120}\)
\(= 8\)

Answer is A
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Re: By selling 12 toffees for a dollar, a shopkeeper loses 20% [#permalink]
03 Oct 2021, 04:58
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