Home / Aptitude Tests / Mathematics / If pq + 1 = q2 and t...
If pq + 1 = q2 and t = \(\frac{1}{p}\) - \(\frac{...

If pq + 1 = q2 and t = \(\frac{1}{p}\) - \(\frac{1}{pq}\) express t in terms of q

A.

\(\frac{1}{p - q}\)

B.

\(\frac{1}{q - 1}\)

C.

\(\frac{1}{q + 1}\)

D.

1 + 0

E.

\(\frac{1}{1 - q}\)

Correct answer is C

Pq + 1 = q2......(i)

t = \(\frac{1}{p}\) - \(\frac{1}{pq}\).........(ii)

p = \(\frac{q^2 - 1}{q}\)

Sub for p in equation (ii)

t = \(\frac{1}{q^2 - \frac{1}{q}}\) - \(\frac{1}{\frac{q^2 - 1}{q} \times q}\)

t = \(\frac{q}{q^2 - 1}\) - \(\frac{1}{q^2 - 1}\)

t = \(\frac{q - 1}{q^2 - 1}\)

= \(\frac{q - 1}{(q + 1)(q - 1)}\)

= \(\frac{1}{q + 1}\)