Proportion Concept

Question

Hi,
Need to need to approach to solve this kind of problem...

P varies as the product of Q & R. If P is trebled and Q is halved, what is change in R?

shrouded1 · Answer

P varies as the product of Q & R :   This statement can be re-written as P=kQR where k is a constant

If P is trebled and Q is halved, what is change in R 
 P_1=kQ_1R_1 
 P_2=3P_1; Q_2=0.5Q_1 
 P_2=kQ_2R_2 
 3P_1=0.5kQ_1R_2 
Dividing,
 0.5R_2/R_1 = 3 
 R_2=6R_1

Sarang · Answer

P=QR
R=P/Q

After amendments, 
R= 3P/Q/2= 6P/Q

Thus new R is 6 times the original R.

KarishmaB · Answer

When we say that P varies directly with Q, we mean that when P increases, Q increases proportionally. When P decreases, Q decreases proportionally. The word proportionally means that if P doubles, Q also doubles. If P becomes 1/3, Q also becomes 1/3
Mathematically, we write this as P α Q or P = kQ

e.g. The cost of renting a hall varies directly with the time for which it is rented. This means Cost = k*Time where k is a constant or Cost/Time = k, a constant.
If you rent the hall for 1 hr, you pay $100. How much will you pay if you rent it for 4 hrs?
If C = 100, T = 1, then k = 100/1 = 100
Now, if T = 4, what is C? C = kT, therefore, C = 100*4 = $400

There is also inverse variation. P varies inversely with Q means when P increases, Q decreasea proportionally and vice versa.
Mathematically, P α 1/Q or PQ = k.

e.g. The cost of a standard gold coin is inversely proportional to the amount of impurities in it. So Cost * Impurities = k.
If a standard gold coin has 4 gm impurities, its cost is $400. What is the amount of impurities in a $ 1200 coin.
So, 4 * 400 = k = x * 1200
x = 4/3 gm

This is how you deal with variation. Your questions states P varies as product of Q and R. (directly is implied here)
P = k*Q*R

\frac{P}{QR} = k = \frac{3P}{(Q/2)R'} 
P and Q get canceled and you get R' = 6R
So R increases by 5R.

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