Lakshya Education MCQs

Question:

The certain worth of a certain sum due sometime hence is Rs. 1600 and the true discount is Rs. 160. The bankers gain is:

Options:
A.Rs. 20
B.Rs. 24
C.Rs. 16
D.Rs. 12
Answer: Option C

B.G. = \(\frac{(T.D.)}{P.W.}^{2} = Rs. \left(\frac{160\times160}{1600}\right) = Rs. 16.\)

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More Questions on This Topic :

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:
  1.    Rs. 360
  2.    Rs. 432
  3.    Rs. 540
  4.    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:
  1.    Rs. 960
  2.    Rs. 840
  3.    Rs. 1020
  4.    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:
  1.    10%
  2.    13%
  3.    12%
  4.    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:
  1.    Rs. 37
  2.    Rs. 37.62
  3.    Rs. 34.38
  4.    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 5.

The bankers gain on a bill due 1 year hence at 12% per annum is Rs. 6. The true discount is:

Options:
  1.    Rs. 72
  2.    Rs. 36
  3.    Rs. 54
  4.    Rs. 50
Answer: Option D

T.D. = \(\frac{B.G.\times100}{R\times T} = Rs. \left(\frac{6\times100}{12\times1}\right) = Rs. 50.\)

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:
  1.    \(5\frac{1}{5}\) %
  2.    \(9\frac{1}{11}\) %
  3.      \(8\frac{1}{8}\)%
  4.      \(6\frac{1}{6}\) %
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 =    \(\left(\frac{100\times1}{\frac{22}{3}\times\frac{3}{2}}\right)\)  % =  \(\frac{10c}{11} \)   = \(9\frac{9}{11}\)   %