The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:Rs. 400Rs. 360Rs. 480Rs. 320
Question
The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:Rs. 400Rs. 360Rs. 480Rs. 320
Solution
The Banker's Discount (BD) and True Discount (TD) are related by the formula:
BD = TD + (TD * r * t)
where r is the rate of interest and t is the time.
Given in the problem: BD = Rs. 420 r = 15% per annum = 15/100 per annum = 0.15 per annum t = 4 months = 4/12 years = 1/3 years
Substituting these values into the formula, we get:
420 = TD + (TD * 0.15 * 1/3)
Solving this equation for TD, we get:
TD = 420 / (1 + 0.15 * 1/3) TD = 420 / (1 + 0.05) TD = 420 / 1.05 TD = Rs. 400
So, the True Discount is Rs. 400.
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