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Two buildings of equal height start sinking into the ground at the sam

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Two buildings of equal height start sinking into the ground at the sam  [#permalink]

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New post 02 Mar 2018, 07:01
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Two buildings of equal height start sinking into the ground at the same time at a uniform rate. One of the buildings will take 16 days and the other 24 days to sink completely. After how many days will the height of the portion above the ground of one of the buildings is exactly twice that of the other building?

A) 5
B) 6
C) 8
D) 10
E) 12
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Re: Two buildings of equal height start sinking into the ground at the sam  [#permalink]

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New post 02 Mar 2018, 08:12
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sameersaluja wrote:
Two buildings of equal height start sinking into the ground at the same time at a uniform rate. One of the buildings will take 16 days and the other 24 days to sink completely. After how many days will the height of the portion above the ground of one of the buildings is exactly twice that of the other building?

A) 5
B) 6
C) 8
D) 10
E) 12

Please help with the analysis



Hi....
Let the height of building be 48m.. 48 is a smart number as it is related to both 16 and 24 as their LCM

so A building goes down by 48/16 or 3 m in one day and building B by 48/24 = 2m

let the condition of twice height is met after x days..
so \(48-2x=2(48-3x)............48-2x=96-6x.........4x=48...............x=12\)days

E
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Re: Two buildings of equal height start sinking into the ground at the sam  [#permalink]

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New post 02 Mar 2018, 07:58
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Ans is E

After 12 days,

one building is sunk to half---
another to 3/4th

so clearly unsunk part of one building is twice the other.
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Re: Two buildings of equal height start sinking into the ground at the sam  [#permalink]

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New post 06 Mar 2018, 07:58
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sameersaluja wrote:
Two buildings of equal height start sinking into the ground at the same time at a uniform rate. One of the buildings will take 16 days and the other 24 days to sink completely. After how many days will the height of the portion above the ground of one of the buildings is exactly twice that of the other building?

A) 5
B) 6
C) 8
D) 10
E) 12


We can let the height of each building be 48 meters. Thus, one building will sink at a rate of 3 meters per day while the other 2 meters per day. We can let n = the number of days it takes for the height of the building (sinking at 2 meters per day) above ground be twice that of the building (sinking at 3 meters per day). We can create the following equation:

2(48 - 3n) = 48 - 2n

48 - 3n = 24 - n

24 = 2n

12 = n

(Note that we chose the height of each building to be 48 feet because 48 is the least common multiple of 16 and 24. This made the arithmetic easy. However, we could have chosen any value for the height of each building, and the answer of 12 days still would have been obtained.)

Answer: E
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Two buildings of equal height start sinking into the ground at the sam  [#permalink]

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New post 20 Apr 2018, 05:05
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sameersaluja wrote:
Two buildings of equal height start sinking into the ground at the same time at a uniform rate. One of the buildings will take 16 days and the other 24 days to sink completely. After how many days will the height of the portion above the ground of one of the buildings is exactly twice that of the other building?

A) 5
B) 6
C) 8
D) 10
E) 12


\((1-\frac{x}{16})*2=1-\frac{x}{24}\)
\(x=12\)

Answer: C
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Two buildings of equal height start sinking into the ground at the sam  [#permalink]

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New post 20 Apr 2018, 15:19
sameersaluja wrote:
Two buildings of equal height start sinking into the ground at the same time at a uniform rate. One of the buildings will take 16 days and the other 24 days to sink completely. After how many days will the height of the portion above the ground of one of the buildings is exactly twice that of the other building?

A) 5
B) 6
C) 8
D) 10
E) 12


sinking rate of slower building=16/24, or 2/3, of faster building
when faster building has sunk 3/4, or 6/8,
slower building has sunk 4/8, or 1/2
slower building retains 1-1/2, or 1/2, above ground
faster building retains 1-3/4, or 1/4, above ground
(1/2)/(1/4)=2
let t=time
t(1/16)=3/4
t=12 days
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Re: Two buildings of equal height start sinking into the ground at the sam  [#permalink]

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New post 20 Apr 2018, 19:38
Hi guys - My answer to this question is 8 instead of 12. I need someone to review the calculation

Each building rate is equal. lets assume x is the height of the building A and x+h is the height of building B.
So, X/16 = (x+h)/24. that implies h=x/2.

Building A height x. Building B height 3x/2.
Rate of each building is x/16

Since it is given as for k days, building B left over height = 2 x building A left over height.
which means
{3x/2-(x/16)*k} = 2 {x-(x/16)*k}
which will bring k = 8 days.
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Two buildings of equal height start sinking into the ground at the sam  [#permalink]

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New post 20 Apr 2018, 21:13
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bhargavasrikantha wrote:
Hi guys - My answer to this question is 8 instead of 12. I need someone to review the calculation

Each building rate is equal. lets assume x is the height of the building A and x+h is the height of building B.
So, X/16 = (x+h)/24. that implies h=x/2.

Building A height x. Building B height 3x/2.
Rate of each building is x/16

Since it is given as for k days, building B left over height = 2 x building A left over height.
which means
{3x/2-(x/16)*k} = 2 {x-(x/16)*k}
which will bring k = 8 days.


bhargavasrikantha
In Question stem , it is given that building heights are same.
Rate of sinking is uniform, not equal as both same height buildings are sinking in different number of days.
Buildings have started sinking at same time.

In your calculation ,you have taken building heights as different to each other , rate of sinking of each building as same.
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Re: Two buildings of equal height start sinking into the ground at the sam  [#permalink]

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New post 21 Apr 2018, 03:40
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thank you. I missed important part of question. Thanks for clarifying
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Re: Two buildings of equal height start sinking into the ground at the sam &nbs [#permalink] 21 Apr 2018, 03:40
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