Find the face value from banker’s gain: The banker’s gain on a bill due 1 year 4 months hence at 7.5% per annum (simple interest) is ₹16. Find the face value of the bill.

Introduction / Context:
Banker’s Gain depends on the square of r t. With BG and r t known, the face value A is obtained directly from BG = A * (r t)^2 / (1 + r t).

Given Data / Assumptions:

• t = 1 year 4 months = 16 months = 4/3 years
• r = 7.5% = 0.075 per annum
• Thus r t = 0.075 * (4/3) = 0.10
• BG = ₹16

Concept / Approach:

Step-by-Step Solution:

Verification / Alternative check:
BD = A * r t = 1760 * 0.10 = ₹176; TD = BD − BG = 176 − 16 = ₹160; TD = A * 0.10 / 1.10 = ₹160 (consistent).

Final Answer:
Rs. 1760