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__Question 1.__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:

**Options:**

- Rs. 360
- Rs. 432
- Rs. 540
- Rs. 1080

**Answer: Option A**

Sum = \( \frac{B.D.\times T.D.}{B.D.-T.D.}=Rs. \left(\frac{72\times60}{72-60}\right)= Rs.\left(\frac{72\times60}{60}\right)= Rs. 360.\)

__Question 2.__The bankers gain on a sum due 3 years hence at 12% per annum is Rs. 270. The bankers discount is:

**Options:**

- Rs. 960
- Rs. 840
- Rs. 1020
- Rs. 760

**Answer: Option C**

T.D. = \(\left(\frac{B.G.\times100}{R\times T}\right)=Rs. \left(\frac{270\times100}{12\times3}\right)= Rs. 750\)

B.D. = Rs.(750 + 270) = Rs. 1020.

__Question 3.__The bankers discount on a sum of money for 1 \(\frac{1}{2}\) years is Rs. 558 and the true discount on the same sum for 2 years is Rs. 600. The rate percent is:

**Options:**

- 10%
- 13%
- 12%
- 15%

**Answer: Option C**

B.D. for \(\frac{3}{2}\)years = Rs. 558

B.D. for 2 years = Rs. \(\left(558\times\frac{2}{3}\times2\right)\)

= Rs.744

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

So, Sum = \(\frac{B.D.\times T.D.}{B.D.- T.D.} = Rs.\left(\frac{744\times600}{144}\right) = Rs. 3100\)

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

Therefore Rate = \( \left(\frac{100\times744}{3100\times2}\right)\) % = 12 %

__Question 4.__The present worth of a certain bill due sometime hence is Rs. 800 and the true discount is Rs. 36. The bankers discount is:

**Options:**

- Rs. 37
- Rs. 37.62
- Rs. 34.38
- Rs. 38.98

**Answer: Option B**

B.G. = \(\frac{(T.D.)}{P.W.}^{2} = Rs. \left(\frac{36\times36}{800}\right) = Rs. 1.62\)

So, B.D. = (T.D. + B.G.) = Rs. (36 + 1.62) = Rs. 37.62

__Question 6.__The bankers gain on a certain sum due 1 \(\frac{1}{2}\) years hence is \(\frac{3}{25}\) of the bankers discount. The rate percent is:

**Options:**

- \(5\frac{1}{5}\) %
- \(9\frac{1}{11}\) %
- \(8\frac{1}{8}\)%
- \(6\frac{1}{6}\) %

**Answer: Option B**

Let, B.D = Re. 1.

Then, B.G. = Re. \(\frac{3}{25}\)

So, T.D. = (B.D. - B.G.) = Re. \(\left(1-\frac{3}{25}\right) = Re. \frac{22}{25}.\)

Sum \(\left(\frac{1\times \left(\frac{22}{25}\right)}{1-\left(\frac{22}{25}\right)}\right) = Rs.\frac{22}{3}\)

S.I. on Rs. \(\frac{22}{3}\) for \(1\frac{1}{2}\) years is Re.1.

So , Rate = \(\left(\frac{100\times1}{\frac{22}{3}\times\frac{3}{2}}\right)\) % = \(\frac{10c}{11} \) = \(9\frac{9}{11}\) %

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