# Average - Aptitude Questions and Answers - RejinpaulPlacement

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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: (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?

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.

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: (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: (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: (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?