Applied Test Series

Question

Three quantities P, Q and R are such that PQ = KR, where K is a constant. When P is kept constant, Q varies directly as R; when Q is kept constant, P varies directly as R and when R is kept constant, P varies directly as Q. Initially, P was at 25 and P : Q : R was 1 : 9 : 25. Find the value of P when Q equals 81 at constant R.

Comments

I am not understanding how can P vary directly as Q if R is kept constant.

Since PQ = KR. Here if RHS is constant then P = C/Q where C = KR.

P is varying inversely as Q.

Answer 1

We label the initial values as P1 (=25), Q1, R1

Initially, P : Q : R = 1 : 9 : 25

So: Q1 = 225 and R1 = 625

As PQ = KR ------ (1),

solving for K gives us:

K = 9 (which is a constant)

 

In the next state assume the values are:

P2 (unknown),

Q2 (=81) and

R2 (=R1 because we assumed constant R)

Plugging in these values in (1):

We have: 81. P2 = 9 . R1

which gives us P2 = $\frac{625}{9}$