In a certain formula, p is directly proportional to s and

Question

In a certain formula, p is directly proportional to s and inversely proportional to r. If p =1 when r = 0.5 and s = 2, what is the value of p in terms of r, and s?

(A) s/r
(B) r/4s
(C) s/4r
(D) r/s
(E) 4r/s

Bunuel · Accepted Answer

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maliyeci · Answer

P is directly proportional to s means => p = x times s (as s increases p increases, x is constant)
P is inversely proportional to r means => p = y divided by r (as r increases p decreases, y is constant)
So we can say 
p= z times s divided by r (z is a constant different from x and y)
When p=1, s =2 and r=0,5
So 1= z*2/0,5
z= 1/4
So p = 1/4*s/r=s/4r

C

vannu · Answer

p is directly proportional to s
p is inversely proportional to r

p=s/r
1= x*2 / 0.5
1=x * 4
Therefore x = 1/4

Hence p=s/4r
The OA is C

JeroenReunis · Answer

P is directly proportional to s means => p = x times s (as s increases p increases, x is constant)
P is inversely proportional to r means => p = y divided by r (as r increases p decreases, y is constant)
So we can say 
p= z times s divided by r  (z is a constant different from x and y) 
When p=1, s =2 and r=0,5
So 1= z*2/0,5
z= 1/4
So p = 1/4*s/r=s/4r

In the below stated question the direct proportional and inverse proportional are combined. Because there is written the word "AND" How does this differ from this question? In other word; Why is the "Z" there in this question?

If the price of a commodity is directly proportional to m^3 and inversely proportional to q^2, which of the following values of m and q will result in the highest price for the commodity?

Thanks in advance for reply!

IshanSaini · Answer

Hoping that this explanation helps :

P is directly proportional to S. 
P is inversely proportional to R.

P -- S
P -- 1/R

So summing it up p -- S/R
Now to equalize it, let us introduce a constant k :
Making P = k * S/R. ------------------- (1)

so the value of the constant k is : k = (P * R)/S

Substitute the values as mentioned in the question :
k = (1 * 0.5)/2 = (1 * 5)/(2*10) = 1/4.

Replace this constant in the first equation --(1).
We get P = S/4R

which is C.

(A) s/r
(B) r/4s
 (C) s/4r 
(D) r/s
(E) 4r/s

bishal128 · Answer

Question states s is proportional to P and r is inversly proportional to P.   thus any expression representing P violating this must be a wrong answer, therefore, option B, D and E is eliminated. Now remaining A and B for the given value of "s" and "r" must satisfy the resulting value of p =1,

A--> s/r = 2/(1/0.5)=4
C--> s/4r=2/4*(1/0.5)=1

Hence the correct answer is C

Mathematically

P ∝ s/r since ratio prduce the constant, hence, the equation form can be written as P=k*s/r 
Pluggin in the value of s and r, 
P= K* 2/(1/0.5) =K*4, hence constant K=1/4 for P=1, 
now,
to generalize, 
P=K*s/r  
P=1/4*s/r=s/4r
Hence, correct answer is option C

In a certain formula, p is directly proportional to s and

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In a certain formula, p is directly proportional to s and

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