On a bill due 4 months hence at 15% p.a., the banker's discount is ₹420. What is the true discount?

Given data

• Time t = 4 months = 1÷3 year; rate r = 15% p.a.
• BD = ₹420.

Concept/Approach
BD = S r t ⇒ find face value S, then TD = S r t ÷ (1 + r t).

Step-by-Step calculation
BD = S × 0.15 × (1÷3) = S × 0.05 = 420 S = 420 ÷ 0.05 = ₹8400 TD = S × 0.05 ÷ (1 + 0.05) = 420 ÷ 1.05 = ₹400

Verification/Alternative
Relation BD ÷ TD = 1 + r t = 1.05 ⇒ TD = BD ÷ 1.05 = 420 ÷ 1.05 = ₹400.

Final Answer
₹400