Aptitude True DiscountPage 2
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:  (a)6 months  (b)8 months  (c)9 months  (d)10 months 

Answer is: DP.W. = Rs. (1760 160) = Rs. 1600.
S.I. on Rs. 1600 at 12% is Rs. 160.
Time = (100 x 160)/(1600 x 12) = 5/6 years
Time = (5/6) x 12 months = 10 months
10.  Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true
discount on the same sum due after half of the former time, the rate of interest being the same?  (a)Rs. 10  (b)Rs. 10.40  (c)Rs. 15.20  (d)Rs. 13 

Answer is: BS.I. on Rs. (260  20) for a given time = Rs. 20.
S.I. on Rs. 240 for half the time = Rs. 10.
T.D. on Rs. 250 = Rs. 10.
T.D. on Rs. 260 = Rs.[10/250] x 260 = Rs. 10.40
11.  The interest on Rs. 750 for 2 years is the same as the true discount on Rs. 960 due 2 years hence. If the rate of interest is the same in both cases, it is:  (a)12%  (b)14%  (c)15%  (d)16% 

Answer is: BS.I. on Rs. 750 = T.D. on Rs. 960.
This means P.W. of Rs. 960 due 2 years hence is Rs. 750.
T.D. = Rs. (960  750) = Rs. 210.
Thus, S.I. on R.s 750 for 2 years is Rs. 210.
Rate = [(100 x 210)/(750 x 2)]% = 14%
12.  Find the present worth of Rs. 930 due 3 years hence at 8% per annum. Also find the discount.  (a)120  (b)150  (c)180  (d)200 

Answer is: CP.W=100 x Amount /[100 + (R x T)]
Rs.[(100 x 930)/100+ (8x3)] = (100x930)/124 = Rs. 750,
T.D. = (Amount)  (P.W.) = Rs. (930  750) = Rs. 180.
13.  The true discount on a certain sum of money due 3 years hence is Rs. 250 and the simple interest on the same sum for the same time and at the same rate is Rs. 375. Find the sum and the rate percent.  (a)16(2/3)%  (b)16%  (c)17(2/3)%  (d)17% 

Answer is: AT.D. = Rs. 250 and S.I. = Rs. 375
Sum due = (S.I. x T.D)/(S.I.  T.D.)
Sum due = (375 x 250)/(375 250)
Sum due =Rs.750.
Rate=[(100 x 375)/(750 x 3)]%=16(2/3)%
14.  The difference between the simple interest and true discount on a certain sum of money for 6 months at 12% per annum is Rs. 25. Find sum.  (a)Rs. 6000  (b)Rs. 6500  (c)Rs. 6800  (d)Rs. 7000 

Answer is: CLet the sum be Rs. X. Then,
T.D. = [X x (25/2) x (1/2)]/[100+(25/2) x (1/2)]
X x (25/4) x (4/425) = X/17
S.I= X x (25/2) x (1/2) x (1/100) = X/16
X/16  X/17 = 25
17 X  16X = 25 x 16 x 17
X = 6800
Hence, sum due = Rs. 6800.
15.  The present worth of Rs. 2310 due 2 years hence, the rate of interest being 15% per annum, is:  (a)1750  (b)1680  (c)1840  (d)1444.75 

Answer is: BP.W. = Rs.[(100 x 2310)/(100 + 15 x (5/2))] = Rs. 1680
16.  The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively. The sum is:  (a)Rs. 1800  (b)Rs. 1450  (c)Rs. 1360  (d)Rs. 6800 

Answer is: CSum = (S.I. x T.D.)/[(S.I.)  (T.D.)]
Sum = [85 x 80]/[85  80] = Rs. 1360
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