With a given rate of simple interest, the ratio of principal and amoun

1.	With a given rate of simple interest, the ratio of principal and amount for a certain period of time is 4 : 5. After 3 years, with the same rate of interest, the ratio of the principal and amount becomes 5 : 7. The rate of interest per annum is (a) 4% (b) 5% (c) 6% (d) 7%
Answer» (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.

With a given rate of simple interest, the ratio of principal and amount for a certain period of time is 4 : 5. After 3 years, with the same rate of interest, the ratio of the principal and amount becomes 5 : 7. The rate of interest per annum is (a) 4% (b) 5% (c) 6% (d) 7%

Answer»

(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.