Aptitude - Chain Rule - Discussion

Discussion :: Chain Rule - General Questions (Q.No.11)

11. 

A flagstaff 17.5 m high casts a shadow of length 40.25 m. The height of the building, which casts a shadow of length 28.75 m under similar conditions will be:

[A]. 10 m
[B]. 12.5 m
[C]. 17.5 m
[D]. 21.25 m

Answer: Option B

Explanation:

Let the height of the building x metres.

Less lengthy shadow, Less in the height (Direct Proportion)

40.25 : 28.75 :: 17.5 : x       40.25 x x = 28.75 x 17.5

x = 28.75 x 17.5
40.25

x = 12.5


Arnav Gupta said: (Jun 24, 2010)  
How to simplify calculation for quick solution.Please suggest any method.

Mini said: (Jul 18, 2011)  
17.5m cast shadow= 40.25
;. 1m cast shadow= 40.25/17.5= 2.3m
so The height of the building, which casts a shadow of length 28.75m= 28.75/2.3= 12.5m

Litu said: (Mar 13, 2012)  
Why directly proportional?

Milind said: (Feb 20, 2013)  
Friends, apply tan formula
tanA= 17.5/40.25=.43478.

So new height = tanA*28.5=12.39==12.5.

Ganesh said: (Mar 4, 2014)  
17.5m cast shadow = 40.25.
So that considered round figure.
40250/175 = 230.

Which casts a shadow of length 28.75m.
Considered round figure = 28750/230 = 125.
So The height of the building is 12.5.

Balaji said: (Jul 20, 2015)  
Please explain me briefly, I can't understand the question.

Jayesh said: (May 20, 2016)  
Here is the proper solution:

17.5m height can produce 40.25 m length shadow.

So, now it is asked that 28.5m length shadow of what height.

Simply cross multiply,

Height <-> Length.
17.5 <-> 40.25.
? <-> 28.75.

=> 28.75 x 17.5/40.25 = 12.5m -->height.

Anonymous said: (Jun 19, 2016)  
Chain rule for solving the solution is :

Direct proportion means first what we have then what we want.

Indirect proportion means first what we want next what we have.

x always in the second field.

Multiply x with first values equals to multiply with second values.

Shiva said: (Jun 22, 2016)  
How can you say shadows height is directly proportional to the height of the building?

Feyi said: (Aug 10, 2016)  
Let the height be 'a' and length of shadow be 'b'.

The higher the height, the longer the shadow (ie height is directly proportioned to the length of the shadow).

The relationship is a & b.

a = kb (k=proprtionality constant).
k = a/b.
=17.5/40.25.

The question is when b =28.75 what is a?

a = kb.
= (17.5/40.25) * 28.75.
=12.5.

Therefore, the height of the building is 12.5m.

Thanks.

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