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Quantitative Aptitude > Discount

DISCOUNT COMBINED MCQs

Total Questions : 712 | Page 6 of 72 pages
Question 51.

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:

  1.    10%
  2.    13%
  3.    12%
  4.    15%
 Discuss Question
Answer: Option C. -> 12%

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 52.

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

  1.    Rs. 960
  2.    Rs. 840
  3.    Rs. 1020
  4.    Rs. 760
 Discuss Question
Answer: Option C. -> Rs. 1020

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 53.

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:

  1.    Rs. 360
  2.    Rs. 432
  3.    Rs. 540
  4.    Rs. 1080
 Discuss Question
Answer: Option A. -> Rs. 360

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 54.

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

  1.    Rs. 20
  2.    Rs. 24
  3.    Rs. 16
  4.    Rs. 12
 Discuss Question
Answer: Option C. -> Rs. 16

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

Question 55.

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

  1.    Rs. 37
  2.    Rs. 37.62
  3.    Rs. 34.38
  4.    Rs. 38.98
 Discuss Question
Answer: Option B. -> Rs. 37.62

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 56.

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

  1.    Rs. 72
  2.    Rs. 36
  3.    Rs. 54
  4.    Rs. 50
 Discuss Question
Answer: Option D. -> Rs. 50

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

Question 57.

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:

  1.    \(5\frac{1}{5}\) %
  2.    \(9\frac{1}{11}\) %
  3.      \(8\frac{1}{8}\)%
  4.      \(6\frac{1}{6}\) %
 Discuss Question
Answer: Option B. -> \(9\frac{1}{11}\) %

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


 

Question 58.

The present worth of a sum due sometime hence is Rs. 576 and the bankers gain is Rs. 16. The true discount is:

  1.    Rs. 36
  2.    Rs. 72
  3.    Rs. 48
  4.    Rs. 96
 Discuss Question
Answer: Option D. -> Rs. 96

T.D. = P.W. x B.G. = 576 x 16 = 96.

Question 59.

The true discount on a bill of Rs. 540 is Rs. 90. The bankers discount is:

  1.    Rs. 60
  2.    Rs. 108
  3.    Rs. 110
  4.    Rs. 112
 Discuss Question
Answer: Option B. -> Rs. 108

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


So,  S.I. on Rs. 450 = Rs. 90.


S.I. on Rs. 540 = Rs. \(\left(\frac{90}{450\times540}\right) = Rs. 108\)


Therefore B.D. = Rs. 108.

Question 60.

The bankers discount on a certain sum due 2 years hence is \(\frac{11}{10}\) of the true discount The rate percent is:

  1.    11%
  2.    10%
  3.    5%
  4.    5.5%
 Discuss Question
Answer: Option C. -> 5%

Let T.D. be Re. 1.


Then, B.D. = Rs. \(\frac{11}{10}\)  = Rs. 1.10


So, Sum = Rs. \(\left(\frac{1.10\times1}{1.10-1}\right) = Rs. \left(\frac{110}{10}\right) = Rs. 11.\)


So,  S.I. on Rs. 11 for 2 years is Rs. 1.10


So,  Rate =  \(\left(\frac{110\times1.10}{11\times2}\right)\)   %  = 5%

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