Aptitude :: True DiscountPage 1
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:  (a)0%  (b)5%  (c)7.5%  (d)10% 

Answer is: AC.P. = Rs. 3000
S.P. = Rs.[(3600 x 100)/(100) + (10 x 2)] = Rs. 3000.
Gain = 0%.
2.  The true discount on Rs. 2562 due 4 months hence is Rs. 122. The rate percent is:  (a)12%  (b)13%  (c)15%  (d)14% 

Answer is: CP.W. = Rs. (2562  122) = Rs. 2440.
S.I. on Rs. 2440 for 4 months is Rs. 122.
Rate = [(100 x 122)/(2440 x 1/3)]% = 15%
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?  (a)9025.50  (b)9200  (c)9600  (d)9560.20 

Answer is: BRequired money= P.W. of Rs. 10028 due 9 months hence =
Rs.[(10028 x 100)/(100 + 12 x (9/12)] = Rs. 9200.
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?  (a)12,000 in cash  (b)12,880 at credit  (c)Both are equally good  (d)Nil 

Answer is: AP.W. of Rs. 12,880 due 8 months hence= Rs.[(12880 x 100)/(100 + 18 x (8/12)]
P.W. of Rs. 12,880 due 8 months hence = Rs. (12880 x 100)/112
P.W. of Rs. 12,880 due 8 months hence = Rs. 11500
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:  (a)20  (b)21.80  (c)22  (d)18.33 

Answer is: DS.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.
T.D. on Rs. 110 = Rs.(20/120) x 110 = Rs. 18.33
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:  (a)16(2/3)%  (b)14(1/2)%  (c)13(1/3)%  (d)15% 

Answer is: AS.P. = 102% of Rs. 600 = [(102/100) x 600] = Rs. 612.
Now, P.W. = Rs. 612 and sum = Rs. 688.50.
T.D. = Rs. (688.50  612) = Rs. 76.50.
Thus, S.I. on Rs. 612 for 9 months is Rs. 76.50.
Rate = [(100 x 76.50)/(612 x 3/4)]% = 16(2/3)%
7.  The true discount on a bill due 9 months hence at 16% per annum is Rs. 189. The amount of the bill is:  (a)1386  (b)1764  (c)1575  (d)2268 

Answer is: BLet P.W. be Rs. X
Then, S.I. on Rs. x at 16% for 9 months = Rs. 189.
X x 16 x (9/12) x (1/100) = 189 or X = 1575.
P.W. = Rs. 1575.
Sum due = P.W. + T.D. = Rs. (1575 + 189) = Rs. 1764.
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:  (a)Gains Rs. 55  (b)Gains Rs. 50  (c)Gains Rs. 30  (d)Loses Rs. 30 

Answer is: BS.P.= P.W. of Rs. 2200 due 1 year hence = Rs. [(2200 x 100)/(100 + (10 x 1))]
S.P.= P.W. of Rs. 2200 due 1 year hence = Rs. 2000.
Gain = Rs. (2000  1950) = Rs. 50.
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