Banker's discount for 1½ years is Rs. 558 and true discount for 2 years is Rs. 600. Find the annual rate of interest.

Given data

• BD (1.5 years) = Rs. 558
• TD (2 years) = Rs. 600
• Rate r = ? per annum; Sum due (A) = unknown

Concept/Approach
Use definitions under simple interest:BD = A × r × t / 100TD = A × r × t / (100 + r t)Form two equations and eliminate A.

Step-by-step calculation
BD: A × r × 1.5 / 100 = 558 ⇒ A r = 558 × 100 / 1.5 = 37,200TD: A × (2r) / (100 + 2r) = 600 ⇒ 600(100 + 2r) = 2 A r600(100 + 2r) = 2 × 37,200 = 74,40060,000 + 1,200 r = 74,400 ⇒ r = 12%

Verification/Alternative
With r = 12%, TD (2y): A × 24 / (100 + 24) = A × 24/124 = 600 ⇒ A = 3,100; BD (1.5y): 3100 × 18/100 = 558 (checks).

Common pitfalls
Plugging BD formula for TD or mixing the times 1.5 and 2 incorrectly.

Final Answer
12%