Pariksha SaathiBanker’s Discount and True Discount Questions with Solutions
A bill due in the future is worth less today — True Discount measures that gap properly, while a banker who pays out immediately charges simple interest on the full future amount instead, which is always a little more. Here’s the concept, four fully worked examples, and a few to try yourself.
The concept, quickly
- Present Worth (PW) is the sum which, invested today at the given rate, would grow into the Amount (A) due at the future date. True Discount (TD) = A − PW.
- Formula: PW = 100×A / (100 + R×T), so TD = A − PW, where R is the annual rate and T is the time in years.
- Banker’s Discount (BD) is simpler but less accurate — it’s just the simple interest on the full future Amount for the unexpired time: BD = A×R×T / 100. BD is always ≥ TD.
- Banker’s Gain (BG) = BD − TD — the extra the banker effectively earns by charging interest on the full future amount instead of the smaller present worth.
Worked examples
1. Find the present worth (PW) and the true discount (TD) on ₹1,200 due 2 years hence at 10% per annum simple interest.
Solution
- PW = 100 × 1,200 / (100 + 10×2) = 120,000 / 120 = ₹1,000.
- TD = A − PW = 1,200 − 1,000 = ₹200.
Answer: PW = ₹1,000, TD = ₹200
2. Find the banker’s discount (BD) on ₹1,200 due 2 years hence at 10% per annum.
Solution
- BD = A×R×T / 100 = 1,200 × 10 × 2 / 100 = ₹240.
Answer: ₹240
3. For the same bill, BD = ₹240 and TD = ₹200. Find the banker’s gain (BG).
Solution
- BG = BD − TD = 240 − 200 = ₹40.
Answer: ₹40
4. The banker’s discount on a bill due 2 years hence at 10% per annum is ₹360. Find the true discount.
Solution
- From BD, find the Amount first: A = BD × 100 / (R×T) = 360 × 100 / 20 = ₹1,800.
- TD = A × R×T / (100 + R×T) = 1,800 × 20 / 120 = ₹300.
Answer: ₹300
Try these yourself
Work out the Amount if it isn’t given directly, then apply the PW/TD/BD formulas, and check against the answer.
1. Find the present worth and the true discount on ₹2,400 due 2 years hence at 10% per annum simple interest.
Answer: PW = ₹2,000, TD = ₹400
2. Find the banker’s discount on ₹2,400 due 2 years hence at 10% per annum.
Answer: ₹480
3. The banker’s discount on a bill due 2 years hence at 10% per annum is ₹480. Find the true discount.
Answer: ₹400
Where this comes up
Banker’s Discount and True Discount is a sub-topic within the Quantitative/Numerical Aptitude section of exams Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk — appearing less frequently than Simple/Compound Interest but still tested.
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