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Aptitude Bankers Discount Test Yourself

2496.The bankers gain on a sum due 6 years hence at 12% per annum is Rs. 540. What is the bankers discount?
1240
1120
1190
1290
Explanation:

$TD = \dfrac{BG \times 100} {TR}$

$=\dfrac{540 \times 100}{6 \times 12}= \dfrac{90 \times 100}{12}$

$= \dfrac{15 \times 100}{2} = Rs.750$

BG = BD - TD

=> 540 = BD - 750

=> BD = 540 + 750 = 1290

2497.The bankers gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. The present worth is:
Rs. 480
Rs. 520
Rs. 600
Rs. 960
Explanation:
T.D. =$ \left(\dfrac{B.G. \times 100}{Rate \times Time} \right) $= Rs.$ \left(\dfrac{24 \times 100}{10 \times 2} \right) $= Rs. 120.
$\therefore$ P.W. =$ \dfrac{100 \times T.D.}{Rate \times Time} $= Rs.$ \left(\dfrac{100 \times 120}{10 \times 2} \right) $= Rs. 600.
2498.The bankers gain on a certain sum due $1\dfrac{1}{2} $years hence is $\dfrac{3}{25}$ of the bankers discount.The rate percent is:
5$ \dfrac{1}{5} $%
9$ \dfrac{1}{11} $%
8$ \dfrac{1}{8} $%
6$ \dfrac{1}{6} $%
Explanation:

Let, B.D = Re. 1.

Then, B.G. = Re.$ \dfrac{3}{25} $.
$\therefore$ T.D. = (B.D. - B.G.) = Re.$ \left(1 -\dfrac{3}{25} \right) $= Re.$ \dfrac{22}{25} $.
Sum =$ \left(\dfrac{1 \times (22/25)}{1-(22/25)} \right) $= Rs.$ \dfrac{22}{3} $.
S.I. on Rs.$ \dfrac{22}{3} $for 1$ \dfrac{1}{2} $years is Re. 1.
$\therefore$ Rate = $\left(\dfrac{100\times1}{22/3\times3/2}\right)$ % =$ \dfrac{100}{11} $= 9$ \dfrac{1}{11} $%.
2499.What is the bankers discount if the true discount on a bill of Rs.540 is Rs.90 ?
Rs. 108
Rs. 120
Rs. 102
Rs. 106
Explanation:

Present Worth, PW = F - TD = 540 - 90 = Rs. 450

Simple Interest on the Present Worth = True Discount

Hence Simple Interest on 450 = 90 ------[Equation 1]

Simple Interest on the face value = Bankers Discount

=> Simple Interest on 540 = Bankers Discount

From Equation 1, Simple Interest on 450 = 90

Hence, Simple Interest on 540 = $\dfrac{90}{450} \times 540= \dfrac{540}{5}$ = Rs. 108

=> Bankers Discount = Rs. 108

2500.The bankers discount on a sum of money for 1$ \dfrac{1}{2} $ years is Rs. 558 and the true discount on the same sum for 2 years is Rs. 600. The rate percent is:
10%
13%
12%
15%
Explanation:
B.D. for $\dfrac{3}{2}$ years = Rs. 558.
B.D. for 2 years = Rs.$ \left(558 \times\dfrac{2}{3} \times 2\right) $
= Rs. 744

T.D. for 2 years = Rs. 600.

$\therefore$ Sum =$ \dfrac{B.D. \times T.D.}{B.D. - T.D} $= Rs.$ \left(\dfrac{744 \times 600}{144} \right) $= Rs. 3100.

Thus, Rs. 744 is S.I. on Rs. 3100 for 2 years.

$\therefore$ Rate =$ \left(\dfrac{100 \times 744}{3100 \times 2} \right) $%= 12%
2501.The present worth of a certain bill due sometime hence is Rs. 800 and the true discount is Rs. 36. The bankers discount is:
Rs. 37
Rs. 37.62
Rs. 34.38
Rs. 38.98
Explanation:
B.G. =$ \dfrac{(T.D.)^2}{P.W.} $= Rs.$ \left(\dfrac{36 \times 36}{800} \right) $= Rs. 1.62

$\therefore$ B.D. = (T.D. + B.G.) = Rs. (36 + 1.62) = Rs. 37.62

2502.The bankers discount of a certain sum of money is Rs. 36 and the true discount on the same sum for the same time is Rs. 30. What is the sum due?
Rs. 180
Rs. 120
Rs. 220
Rs. 200
Explanation:

$F =\dfrac{BD \times TD}{BD - TD}$= $\dfrac{36 \times 30}{(36 - 30)}$

$=\dfrac{36 \times 30}{6} = 36 \times 5 = Rs.180$

2506.The bankers discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is:
3 months
4 months
6 months
8 months
Explanation:

S.I. on Rs. 1600 = T.D. on Rs. 1680.

$\therefore$ Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.

$\therefore$ Time =$ \left(\dfrac{100 \times 80}{1600 \times 15} \right) $year=$ \dfrac{1}{3} $year = 4 months.

2508.The true discount on a bill of Rs. 540 is Rs. 90. The bankers discount is:
Rs. 60
Rs. 108
Rs. 110
Rs. 112
Explanation:

P.W. = Rs. (540 - 90) = Rs. 450.

$\therefore$ S.I. on Rs. 450 = Rs. 90.

S.I. on Rs. 540 = Rs.$ \left(\dfrac{90}{450} \times 540\right) $= Rs. 108.

$\therefore$ B.D. = Rs. 108.

2509.The bankers discount of a certain sum of money is Rs. 72 and the true discount on the same sum for the same time is Rs. 60. The sum due is:
Rs. 360
Rs. 432
Rs. 540
Rs. 1080
Explanation:
Sum =$ \dfrac{B.D. \times T.D.}{B.D. - T.D.} $= Rs.$ \left(\dfrac{72 \times 60}{72 - 60} \right) $= Rs.$ \left(\dfrac{72 \times 60}{12} \right) $= Rs. 360.
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