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True Discount - Aptitude MCQ Questions and Solutions with Explanations

True Discount MCQ Questions and answers with easy and logical explanations.Arithmetic Ability provides you all type of quantitative and competitive aptitude mcq questions on True Discount with easy and logical explanations. True Discount MCQ is important for exams like Banking exams,IBPS,SCC,CAT,XAT,MAT etc.

Each section contains 100 MCQs on True Discount .
1
A man purchased a cow for Rs. 3000 and sold it the same day for Rs. 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of:
Discuss
Answer & Solution
Answer: Option A
Solution:
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{.}} = Rs.\,3000 \cr & {\text{S}}{\text{.P}}{\text{.}} = Rs.\,\left[ {\frac{{3600 \times 100}}{{100 + \left( {10 \times 2} \right)}}} \right] \cr & = Rs.\,3000 \cr & {\text{Gain}} = 0\% \cr} $$
2
The true discount on Rs. 2562 due 4 months hence is Rs. 122. The rate percent is:
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & {\text{P}}{\text{.W}}{\text{.}} = Rs.\left( {2562 - 122} \right) \cr & = Rs.2440 \cr & \therefore {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{2440}}\,{\text{for}}\,{\text{4}}\,{\text{months}}\,{\text{is}}\,{\text{Rs}}{\text{.}}\,{\text{122}}{\text{.}} \cr & \therefore {\text{Rate}} = \left[ {\frac{{100 \times 122}}{{2440 \times \frac{1}{3}}}} \right]\% = 15\% \cr} $$
3
A trader owes a merchant Rs. 10,028 due 1 year hence. The trader wants to settle the account after 3 months. If the rate of interest 12% per annum, how much cash should he pay?
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & {\text{Required}}\,{\text{Money}} \cr & {\text{ = }}\,{\text{P}}{\text{.W}}{\text{.}}\,{\text{of}}\,{\text{Rs}}{\text{.}}\,{\text{10028}}\,{\text{due}}\,{\text{9}}\,{\text{months}}\,{\text{hence}} \cr & = Rs.\,\left[ {\frac{{10028 \times 100}}{{100 + \left( {12 \times \frac{9}{{12}}} \right)}}} \right] \cr & = Rs.\,9200 \cr} $$
4
A man wants to sell his scooter. There are two offers, one at Rs. 12,000 cash and the other a credit of Rs. 12,880 to be paid after 8 months, money being at 18% per annum. Which is the better offer?
Discuss
Answer & Solution
Answer: Option A
Solution:
$$\eqalign{ & {\text{ = }}\,{\text{P}}{\text{.W}}{\text{.}}\,{\text{of}}\,{\text{Rs}}{\text{.}}\,{\text{12,880}}\,{\text{due}}\,{\text{8}}\,{\text{months}}\,{\text{hence}} \cr & = Rs.\,\left[ {\frac{{12880 \times 100}}{{100 + \left( {18 \times \frac{8}{{12}}} \right)}}} \right] \cr & = Rs.\,\left( {\frac{{12880 \times 100}}{{112}}} \right) \cr & = Rs.\,11500 \cr} $$
Clearly 12000 in cash is a better offer.
5
If Rs. 10 be allowed as true discount on a bill of Rs. 110 due at the end of a certain time, then the discount allowed on the same sum due at the end of double the time is:
Discuss
Answer & Solution
Answer: Option D
Solution:
S.I. on Rs. (110 - 10) for a certain time = Rs. 10.
S.I. on Rs. 100 for double the time = Rs. 20.
T.D. on Rs. 120 = Rs. (120 - 100) = Rs. 20.
$$\eqalign{ & {\text{T}}{\text{.D}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{110}} \cr & = Rs.\,\left( {\frac{{20}}{{120}} \times 110} \right) \cr & = Rs.\,18.33 \cr} $$
6
Goods were bought for Rs. 600 and sold the same for Rs. 688.50 at a credit of 9 months and thus gaining 2% The rate of interest per annum is:
Discuss
Answer & Solution
Answer: Option A
Solution:
$$\eqalign{ & {\text{S}}{\text{.P}}{\text{.}} = 102\% \,of\,Rs.\,600 \cr & = {\frac{{102}}{{100}} \times 600} \cr & = Rs.\,612 \cr & {\text{Now,}}\,\cr & {\text{P}}{\text{.W}}{\text{. = Rs}}{\text{. 612}}\,{\text{and}}\,{\text{sum}} = Rs.\,688.50 \cr & \therefore {\text{T}}{\text{.D}}{\text{.}} = Rs.\,\left( {688.50 - 612} \right) \cr & = Rs.\,76.50. \cr & {\text{Thus,}}\,{\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{612}}\,{\text{for}}\,{\text{9}}\,{\text{months}}\,{\text{is}}\,{\text{Rs}}{\text{.}}\,{\text{76}}{\text{.50}}{\text{.}} \cr & \therefore {\text{Rate}} = \left( {\frac{{100 \times 76.50}}{{612 \times \frac{3}{4}}}} \right)\% \cr & = 16\frac{2}{3}\% \, \cr} $$
7
The true discount on a bill due 9 months hence at 16% per annum is Rs. 189. The amount of the bill is:
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & {\text{Let}}\,{\text{P}}{\text{.W}}{\text{.}}\,{\text{be}}\,{\text{Rs}}{\text{.}}\,{\text{x}}{\text{.}} \cr & {\text{Then,}}\,{\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{x}}\,{\text{at}}\,{\text{16}}\% \,{\text{for}}\,{\text{9}}\,{\text{months}} \cr & = Rs.\,189 \cr & \therefore x \times 16 \times \frac{9}{{12}} \times \frac{1}{{100}} \cr & = 189\,or\,x = 1575. \cr & \therefore P.W. = Rs.\,1575. \cr & \therefore {\text{Sum}}\,{\text{due}} = P.W. + T.D. \cr & = Rs.\left( {1575 + 189} \right) \cr & = Rs.\,1764 \cr} $$
8
A man buys a watch for Rs. 1950 in cash and sells it for Rs. 2200 at a credit of 1 year. If the rate of interest is 10% per annum, the man:
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & {\text{S}}{\text{.P}}{\text{. = P}}{\text{.W}}{\text{.}}\,{\text{of}}\,{\text{Rs}}{\text{.}}\,{\text{2200}}\,{\text{due}}\,{\text{1}}\,{\text{year}}\,{\text{hence}} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left[ {\frac{{2200 \times 100}}{{100 + \left( {10 \times 1} \right)}}} \right] \cr & \,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,2000 \cr & \therefore {\text{Gain}} = Rs.\left( {2000 - 1950} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,50 \cr} $$
9
The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160. The time after which it is due is:
Discuss
Answer & Solution
Answer: Option D
Solution:
$$\eqalign{ & P.W. = Rs.\left( {1760 - 160} \right) = Rs.\,1600 \cr & \therefore {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{1600}}\,{\text{at}}\,{\text{12}}\% \,{\text{is}}\,{\text{Rs}}{\text{.}}\,{\text{160}}{\text{}} \cr & \therefore {\text{Time}} = {\frac{{100 \times 160}}{{1600 \times 12}}} \cr & = \frac{5}{6}{\text{years}} \cr & = \left( {\frac{5}{6} \times 12} \right){\text{months}} \cr & = 10\,{\text{months}}{\text{}} \cr} $$
10
The present worth of Rs. 2310 due $$2\frac{1}{2}$$ years hence, the rate of interest being 15% per annum, is:
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & P.W. = Rs.\,\left[ {\frac{{100 \times 2310}}{{100 + \left( {15 \times \frac{5}{2}} \right)}}} \right] \cr & = Rs.\,1680 \cr} $$