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1.
A bill for Rs. 6000 is drawn on July 14 at 5 months . It is discounted on 5th October at 10%. Find the banker's discount, true discount, banker's gain and the money that the holder of the bill receives.
Answer & Solution
Answer: c) Rs. 120, Rs. 117.64, Rs. 2.36, Rs. 5880
Solution: Face value of the bill = Rs. 6000. Date on which the bill was drawn = July 14 at 5 months. Nominally due date = December 14. Legally due date = December 17. Date on which the bill was discounted = October 5. Unexpired time: Oct.+Nov.+Dec. 26 + 30 + 17 = 73 days = 1/5 year. Banker's discount (B.D) = S.I. on Rs. 6000 for 1/5 years = Rs. [6000 * 10 * (1/5) * (1/100)] = Rs. 120. True Discount (T.D) = Rs. [{6000 * 10 * (1/5)} / {100 + {10 * (1/5)}}] = Rs. (12000/102) = Rs. 117.64. Banker's gain (B.G) = (B.D) - (T.D) = Rs. (120 - 117.64) = Rs. 2.36. Money received by the holder of the bill = Rs. (6000 - 120) = Rs. 5880. 
2.
If the true discount on a certain sum due 6 months hence at 15% is Rs. 120, what is the banker's discount on the same sum for the same time and at the same rate?
Answer & Solution
Answer: d) Rs. 129
Solution: B.G = S.I. on T.D = Rs. [120 * 15 * (1/2) * (1/100)] = Rs. 9 (B.D) - (T.D) = Rs. 9. B.D. = Rs. (120 + 9) = Rs. 129.
3.
The banker's discount on Rs. 1800 at 12% per annum is equal to the true discount on Rs. 1872 for the same time at the same rate. Find the time.
Answer & Solution
Answer: b) 4 months
Solution: S.I on Rs. 1800 = T.D. on Rs. 1872. P.W of Rs. 1872 is Rs. 1800. Rs. 72 is S.I. on Rs. 1800 at 12%. Time = [(100 * 72) / (12 * 1800)] year = 1/3 year = 4 months.
4.
The banker's discount and the true discount on a sum of money due 8 months hence are Rs. 120 and Rs. 110 respectively. Find the sum and rate percent.
Answer & Solution
Answer: c) Rs. 1320, 13 7/11 %
Solution: Sum = [(B.D. * T.D.) / (B.D. - T.D)] = Rs. [(120 * 110) / (120 - 110)] = Rs. 1320. Since B.D is S.I. on sum due, so S.I. on Rs. 1320 for 8 months is Rs. 120. Rate = [(100 * 120) / {1320 * (2/3)}] % = 13 7/11 %
5.
The present worth of a bill due sometime hence is Rs. 1100 and the true discount on the bill is Rs. 110. Find the banker's discount and the banker's gain.
Answer & Solution
Answer: b) Rs. 121, Rs. 11
Solution: T.D. = sq.rt (P.W * B.G) B.G = [(T.D)^2 / P.W] = Rs. [(110 * 110) / 1100] = Rs. 11. B.D. = (T.D. + B.G.) = Rs. (110 + 11) = Rs. 121. 6.
The banker's discount on Rs. 1650 due a certain time hence is Rs. 165. Find the true discount and the banker's gain.
Answer & Solution
Answer: c) Rs. 150, Rs. 15
Solution: Sum = [(B.D * T.D) / (B.D - T.D)] = [(B.D * T.D) / B.G] T.D/B.G = Sum / B.D = 1650 / 165 = 10 / 1. Thus, if B.G is Re. 1, T.D = Rs. 10 If B.D is Rs. 11, T.D = Rs. 10. If B.D is Rs. 165, T.D = Rs. [(10/11) * 165] = Rs. 150. And, B.G. = Rs. (165 - 150) = Rs. 15.
7.
What rate percent does a man get for his money when in discounting a bill due 10 months hence, he deducts 10% of the amount of the bill?
Answer & Solution
Answer: b) 13 1/3 %
Solution: Let, amount of the bill = Rs. 100. Money deducted = Rs. 10. Money received by the holder of the bill = Rs. (100 - 10) = Rs. 90. S.I. on Rs. 90 for 10 months = Rs. 10. Rate = [(100 * 10) / {90 * (10/2)}] % = 13 1/3 %.
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