Three amounts P, Q , R are such that Q is the simple interest on P and R is the simple interest on Q. If in all the case, rate of interest per annum and the time for which interest is calculated is the same, then relation between P, Q and R is?

Option 3 : Q2 = PR

Let the rate be r and time be t in both cases.

As given, Q is the SI on P, we can write,

⇒ Q = P ⨯ r ⨯ t/100      ----(1)

Also given that, R is SI on Q, we can write,

⇒ R = Q ⨯ r ⨯ t/100      ----(2)

Dividing equation (2) by equation (1), we get,

⇒ Q/R = P/Q

Option 3 : Q2 = PR

Let the rate be r and time be t in both cases.

As given, Q is the SI on P, we can write,

⇒ Q = P ⨯ r ⨯ t/100      ----- (1)

Also given that, R is SI on Q, we can write,

⇒ R = Q ⨯ r ⨯ t/100     ----- (2)

Dividing equation (2) by equation (1), we get,

⇒ Q/R = P/Q

∴ Q² = PR