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In 1995, the Johnsons spent $800 on the family’s water bills. Anticipa

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Bunuel
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In 1995, the Johnsons spent $800 on the family’s water bills. Anticipa [#permalink] New post   14 Feb 2016, 10:49
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In 1995, the Johnsons spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Johnsons cut back their water usage. By how much must the Johnsons have reduced their 1996 water usage to pay exactly the same amount in 1996 as they paid in 1995?

A. 33 1⁄3%
B. 40%
C. 50%
D. 66 2⁄3%
E. 100%
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A
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Re: In 1995, the Johnsons spent $800 on the family’s water bills. Anticipa [#permalink] New post   14 Feb 2016, 21:02
In 1995 , water usage for Johnsons = w
and cost per unit of water = c
cw = 800
=> w=800/c -- 1

In 1996 , cost per unit of water = 1.5 c
Water usage for Johnsons so as to pay same amount as in 1995= w'
1.5c * w' = 800
=> w' = 800/1.5c
=> w' = (2/3c)*800
From 1 and 2 , we get
w' = 2/3 w
(w-w')/w = 1/3

Answer A
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Re: In 1995, the Johnsons spent $800 on the family’s water bills. Anticipa [#permalink] New post   14 Feb 2016, 22:30
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Bunuel wrote:
In 1995, the Johnsons spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Johnsons cut back their water usage. By how much must the Johnsons have reduced their 1996 water usage to pay exactly the same amount in 1996 as they paid in 1995?

A. 33 1⁄3%
B. 40%
C. 50%
D. 66 2⁄3%
E. 100%



Total Bill = Rate * Consumption

If rate increases by 50% and becomes (3/2) of initial Rate, Consumption should become (2/3) of initial consumptions so that the Total Bill remains the same.

Total Bill = (3/2) * Rate * (2/3) * Consumption = Rate * Consumption

(2/3) of the initial consumption means a decrease of 1/3 which is 33.33%.

Answer (A)
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In 1995, the Johnsons spent $800 on the family’s water bills. Anticipa [#permalink] New post   14 Feb 2016, 23:30
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Suppose in 1995, water usage = "s" and cost per unit = "c".
So, total spend = sc

Now, in 1996, cost per unit = "1.5c"
Suppose new water usage = X
So, total spend = 1.5cX

Since total spend has to remain the same,

sc = 1.5c X
X = s / 1.5

Hence, percentage reduction in the water usage = [(s - s/1.5)/s ] * 100 = 33.33%

So, it seems there is no real use of the $800 figure, because everything is in percentage terms.
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In 1995, the Johnsons spent $800 on the family’s water bills. Anticipa [#permalink] New post   15 Feb 2016, 22:15
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In 1995 the water bill costs $800
Anticipated bill in 1996 is 50% more of 800$=$1200

Difference of costs ($400 divided by increase in costs $1200(which is taken to retain the original bill amount) )*100= $400/$1200*100= 33.33%
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Re: In 1995, the Johnsons spent $800 on the family’s water bills. Anticipa [#permalink] New post   10 May 2016, 22:27
Can be solved as follows:
1995 total bill = 1996 total bill
notice that for this question the absolute amount does not matter .. as it is asking for the % decrease in consumption
x-consumption in 19951
y-consumption in 1996
p-price per unit of water in 1995
x*p=(3/2)p*y
=> x=3/2*y=> y = 2/3*x=> y is 1/3rd less than x. so the consumption should fall by 1/3 , which is equiv. to 33.33% reduction.
A
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Re: In 1995, the Johnsons spent $800 on the family’s water bills. Anticipa [#permalink] New post   11 May 2016, 02:52
water rate increases by 50 % in 1996 means 150% of rate in 1995. to pay exactly the same amount in 1996 as they paid in 1995, water use should decrease in the same ratio

150-> 100 means 1/3 rd= 33(1/3) %






A. 33 1⁄3%
B. 40%
C. 50%
D. 66 2⁄3%
E. 100%
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Re: In 1995, the Johnsons spent $800 on the family’s water bills. Anticipa [#permalink] New post   25 Dec 2017, 22:06
In 1995, the Johnsons spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Johnsons cut back their water usage. By how much must the Johnsons have reduced their 1996 water usage to pay exactly the same amount in 1996 as they paid in 1995?

A. 33 1⁄3%
B. 40%
C. 50%
D. 66 2⁄3%
E. 100%

c = consumption, r = rate, Annual bill = r*c
For annual bills to be equal r*c = X*r*c*3/2 -> X*3/2 = 1 -> x = 2/3 -> annual decrease in consumption is 1/3 = 33.33%
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In 1995, the Johnsons spent $800 on the family’s water bills. Anticipa [#permalink] New post   27 Oct 2020, 10:40
Bunuel wrote:
In 1995, the Johnsons spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Johnsons cut back their water usage. By how much must the Johnsons have reduced their 1996 water usage to pay exactly the same amount in 1996 as they paid in 1995?

A. 33 1⁄3%
B. 40%
C. 50%
D. 66 2⁄3%
E. 100%

\(\frac{50}{(100-50)}*100\) = \(33\frac{1}{3}\)%, Answer will be (A)
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In 1995, the Johnsons spent $800 on the family’s water bills. Anticipa [#permalink]
27 Oct 2020, 10:40
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