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

Question

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

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

chetan2u · Accepted Answer

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

mygmat0101 · Answer

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.

ScottTargetTestPrep · Answer

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

Tulkin987 · Answer

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

Answer: C

gracie · Answer

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
E

bhargavasrikantha · Answer

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.

Princ · Answer

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.

bhargavasrikantha · Answer

Princ 
thank you. I missed important part of question. Thanks for clarifying

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

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