(b) 5% p.a.
Suppose after t years, P = Rs 4x and Amount = Rs 5x
⇒ P + S.I. after t years = Rs 5x … (i)
Also, given P : [P + S.I. after (t + 3) years]
= 5 : 7 = 1 : \(\frac75\) = 4x : \(\frac75\) x 4x = 4x : \(\frac{28x}{5}\)
⇒ P + S.I. after (t + 3) years = Rs \(\frac{28x}{5}\) ....(ii)
∴ Eq (ii) – Eq (i) gives
S.I. after 3 years = Rs \(\bigg(\frac{28x}{5}-5x\bigg)\) = Rs \(\frac{3x}{5}\)
∴ Rate of interest = \(\frac{\frac{3x}{5}\times100}{4x\times3}\) = 5% p.a.