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Between the first day of May and last day in June, the price per kilog

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Between the first day of May and last day in June, the price per kilog  [#permalink]

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New post 05 Jun 2018, 10:31
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

57% (02:06) correct 43% (02:33) wrong based on 62 sessions

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Between the first day of May and last day in June, the price per kilogram of Melange, a seasoning mix, first declined by 20 percent and then increased by 50 percent. During this same period, the price per liter of Blue, a spring water, first increased by 20 percent and then declined by 50 percent. If at the end of June, the prices were the same, then, at the beginning of May, the price per kilogram for Blue was what percent of the price per liter of Melange?

A. 2
B. 30
C. 50
D. 100
E. 200

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Re: Between the first day of May and last day in June, the price per kilog  [#permalink]

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New post 05 Jun 2018, 10:50

Solution



Given:
    • The price of Melange first declined by 20% and then increased by 50%
    • The price of Blue water first increased by 20% and then declined by 50%
    • At the end, both the prices are same

To find:
    • At the beginning, price of Blue water was what percent of the price of Melange

Approach and Working:
Assuming the initial price of Melange and Blue water was m and b respectively
    • Price of Melange after two changes = m * 0.8 * 1.5 = 1.2 m
    • Price of Blue water after two changes = b * 1.2 * 0.5 = 0.6 b

Given that, the end prices were same. Therefore,
    • 1.2 m = 0.6 b
    Or, \(\frac{b}{m} = \frac{1.2}{0.6} = 2\)
    Or, \(\frac{b}{m} * 100 = 2 * 100 = 200%\)

Hence, the correct answer is option E.

Answer: E
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Re: Between the first day of May and last day in June, the price per kilog  [#permalink]

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New post 27 Nov 2018, 22:58
Hi All,

We're told that a between the first day of May and last day in June, the price per kilogram of Melange, a seasoning mix, first DECLINED by 20 percent and then INCREASED by 50 percent and during this same period, the price per liter of Blue, a spring water, first INCREASED by 20 percent and then DECLINED by 50 percent. We're also told that at the end of June, the prices were the SAME. We're asked, at the beginning of May, the price per kilogram for Blue was what percent of the price per liter of Melange. This question can be solved in a couple of different ways, including by TESTing VALUES and a bit of Arithmetic.

IF... in May...
1 kg of Melange = $100
the 20% decline in price --> $100 - (.2)($100) = 100 - 20 = $80
the 50% increase in price --> $80 + (.5)($80) = 80 + 40 = $120

Using this final price of $120, we can 'work backwards' to figure out the price of Blue in May

Final price of Blue = $120
the 50% decline in price to END at $120 --> (.5)(X) = $120 --> X = $240
the 20% increase to get to $240 --> (1.2Y) = $240 --> Y = $200

In May, the price of 1 kg of Melange = $100 and the price of 1 liter of Blue = $200
200/100 = 2 = 200% the price

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Re: Between the first day of May and last day in June, the price per kilog   [#permalink] 27 Nov 2018, 22:58
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