The simple interest on Rs. 750 for 2 years equals the true discount on Rs. 960 due 2 years hence. Find the common rate per annum.

Interest side

Simple interest = 750 × r × 2 / 100 = 15r

True discount side

For amount A = 960, time t = 2, rate r%:TD = A × (rt)/(100 + rt) = 960 × (2r)/(100 + 2r)

Equate and solve15r = 960 × (2r)/(100 + 2r) ⇒ 15 = 1920/(100 + 2r)100 + 2r = 1920/15 = 128 ⇒ 2r = 28 ⇒ r = 14%

VerificationSI = 15r = 210 when r = 14; TD = 960 × (28)/(128) = 210 — equal.

Final Answer14%