1320.A bill for Rs. 6000 is drawn on July 14 at 5 months. It is discounted on 5th October at 10%. Find the bankers discount, true discount, bankers gain and the money that the holder of the bill receives.
2.36
2
1
3.26
Explanation:
Face value of the bill = Rs. 6000.
Date on which the bill was drawn = July 14 at 5 months. Nominally due date = December 14.
Legally due date = December 17.
Date on which the bill was discounted = October 5.
Unexpired time : Oct. Nov. Dec.
26 + 30 + 17 = 73 days =1/ 5Years
B.D. = S.I. on Rs. 6000 for 1/5 year
= Rs. (6000 x 10 x1/5 x1/100)= Rs. 120.
T.D. = Rs.[(6000 x 10 x1/5)/(100+(10*1/5))]
=Rs.(12000/102)=Rs. 117.64.
B.G. = (B.D.) - (T.D.) = Rs. (120 - 117.64) = Rs. 2.36.
Face value of the bill = Rs. 6000.
Date on which the bill was drawn = July 14 at 5 months. Nominally due date = December 14.
Legally due date = December 17.
Date on which the bill was discounted = October 5.
Unexpired time : Oct. Nov. Dec.
26 + 30 + 17 = 73 days =1/ 5Years
B.D. = S.I. on Rs. 6000 for 1/5 year
= Rs. (6000 x 10 x1/5 x1/100)= Rs. 120.
T.D. = Rs.[(6000 x 10 x1/5)/(100+(10*1/5))]
=Rs.(12000/102)=Rs. 117.64.
B.G. = (B.D.) - (T.D.) = Rs. (120 - 117.64) = Rs. 2.36.
1321.If the true discount on a certain sum due 6 months hence at 15% is Rs. 120, what is the bankers discount on the same.
128
130
129
127
Explanation:
Sol. B.G. = S.I. on T.D.
= Rs.(120 x 15 x 1/2 x 1/100)
= Rs. 9.
(B.D.) - (T.D.) = Rs. 9.
B.D. = Rs. (120 + 9) = Rs. 129.
Sol. B.G. = S.I. on T.D.
= Rs.(120 x 15 x 1/2 x 1/100)
= Rs. 9.
(B.D.) - (T.D.) = Rs. 9.
B.D. = Rs. (120 + 9) = Rs. 129.
1322.The bankers discount on Rs. 1800 at 12% per annum is equal to the true discount on Rs. 1872 for the same time at the same rate. Find the time.
3 months
5 months
1 month
4 months
Explanation:
S.I. on Rs. 1800 = T.D. on Rs. 1872.
P.W. of Rs. 1872 is Rs. 1800.
Rs. 72 is S.I. on Rs. 1800 at 12%.
Time =[(100 x 72)/ (12x1800)]year
1/3year = 4 months.
S.I. on Rs. 1800 = T.D. on Rs. 1872.
P.W. of Rs. 1872 is Rs. 1800.
Rs. 72 is S.I. on Rs. 1800 at 12%.
Time =[(100 x 72)/ (12x1800)]year
1/3year = 4 months.
1323.The bankers discount and the true discount on a sum of money due 8 months hence are Rs. 120 and Rs. 110 respectively.
137/11%
120/12%
136/11%
140/11%
Explanation:
Sum =[( B.D.*T.D.)/(B.D.-T.D.)]
= Rs.[(120x110)/(120-110)]
= Rs. 1320.
Since B.D. is S.I. on sum due, so S.I. on Rs. 1320 for 8 months is Rs. 120.
Rate =[(100 x120)/( 1320 x 2/3)%
= 13 7/11%.
Sum =[( B.D.*T.D.)/(B.D.-T.D.)]
= Rs.[(120x110)/(120-110)]
= Rs. 1320.
Since B.D. is S.I. on sum due, so S.I. on Rs. 1320 for 8 months is Rs. 120.
Rate =[(100 x120)/( 1320 x 2/3)%
= 13 7/11%.
1396.The true discount on a bill due 9 months hence at 12%
per annum is Rs. Find the amount of the bill and its present
worth.
per annum is Rs. Find the amount of the bill and its present
worth.
Rs.6000
Rs.6500
Rs.5500
Rs.6570
Explanation:
Let amount be Rs. x. Then,
x*R*T/100 + (R x T)
=T.D.
=>x * 12*3/ 4/[100+[12*3/4]]
=540
x= 540x109 = Rs.6540
Amount - Rs. 6540. P.W. = Rs. (6540 - 540) - Rs. 6000
Let amount be Rs. x. Then,
x*R*T/100 + (R x T)
=T.D.
=>x * 12*3/ 4/[100+[12*3/4]]
=540
x= 540x109 = Rs.6540
Amount - Rs. 6540. P.W. = Rs. (6540 - 540) - Rs. 6000
1397.The true discount on a certain sum of money due 3 years hence is Rb. 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.
Rate%=16 2/3%
Rate%=17 1/3%
Rate%=16%
Rate%=13 2/3%
Explanation:
T.D. = Rs. 250 and S.I. = Rs. 375.
Sum due =S.I. xT.D./ S.I. -T.D.
=375x250/375- 250
=Rs.750.
Rate=[100*375/750*3]%=16 2/3%
Sum due =S.I. xT.D./ S.I. -T.D.
=375x250/375- 250
=Rs.750.
Rate=[100*375/750*3]%=16 2/3%
1398.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 the sum.
discount on a certain sum of money for 6 months at 12—% per annum is Rs. 25. Find the sum.
Rs. 5400
Rs. 6000
Rs. 6800
None of these
Explanation:
Let the sum be Rs. x. Then,
T.D. = (x*25/2*1/2)/(100+(25/2*1/2))=x*25/4*4/425=x/17
S.I=x*25/2*1/2*1/100=x/16
x/16-x/17=25
=>17x-16x=25*16*17
=>x=6800
Hence, sum due = Rs. 6800.
Let the sum be Rs. x. Then,
T.D. = (x*25/2*1/2)/(100+(25/2*1/2))=x*25/4*4/425=x/17
S.I=x*25/2*1/2*1/100=x/16
x/16-x/17=25
=>17x-16x=25*16*17
=>x=6800
Hence, sum due = Rs. 6800.
1399.A bill falls due in 1 year. The creditor agrees to accept
immediate payment of the half and to defer the payment of the
other half for 2 years. By this arrangement
ins Rs. 40. What is the amount of the bill, if the money be
worth 12-z% ?
immediate payment of the half and to defer the payment of the
other half for 2 years. By this arrangement
ins Rs. 40. What is the amount of the bill, if the money be
worth 12-z% ?
Rs. 3600
Rs. 3000
Rs. 2400
Rs. 1500
Explanation:
Let the sum be Rs. x. Then,
[x/2+(x/2*100)/100+(25/2*2)]-[(x*100)/(100+25/2*1]
=40
=>x/2+2x/5-8x/9=40
=>x=3600
Amount of the bill - Rs. 3600.
Let the sum be Rs. x. Then,
[x/2+(x/2*100)/100+(25/2*2)]-[(x*100)/(100+25/2*1]
=40
=>x/2+2x/5-8x/9=40
=>x=3600
Amount of the bill - Rs. 3600.
1408.The bankers discount and the true discount on a sum of money due 8 months hence are Rs. 120 and Rs. 110 respectively. Find the sum and the rate percent.
rate percent= 13 7/11%
rate percent= 12 5/11%
rate percent= 10 7/11%
None of these
Explanation:
Sum =[( B.D.*T.D.)/(B.D.-T.D.)]
= Rs.[(120x110)/(120-110)]
= Rs. 1320.
Since B.D. is S.I. on sum due, so S.I. on Rs. 1320 for 8 months is Rs. 120.
Rate =[(100 x120)/( 1320 x 2/3)%
= 13 7/11%.
Sum =[( B.D.*T.D.)/(B.D.-T.D.)]
= Rs.[(120x110)/(120-110)]
= Rs. 1320.
Since B.D. is S.I. on sum due, so S.I. on Rs. 1320 for 8 months is Rs. 120.
Rate =[(100 x120)/( 1320 x 2/3)%
= 13 7/11%.
1409.The present worth of a bill due sometime hence is Rs. 1100 and the true discount on the bill is Rs. 110. Find the bankers discount and the bankers gain.
Rs. 110
Rs. 120
Rs. 121
Rs. 115
Explanation:
T.D. =Ö(P.W.*B.G)
B.G. =(T.D.)2/ P.W.
= Rs.[(110x110)/ 1100]
= Rs. 11.
B.D.= (T.D. + B.G.) = Rs. (110 + 11) = Rs. 121.
T.D. =Ö(P.W.*B.G)
B.G. =(T.D.)2/ P.W.
= Rs.[(110x110)/ 1100]
= Rs. 11.
B.D.= (T.D. + B.G.) = Rs. (110 + 11) = Rs. 121.
1410.The bankers discount on Rs. 1650 due a certain time hence is Rs. 165. Find the true discount and the bankers gain.
Rs 15
Rs 16
Rs 14
None of these
Explanation:
Sum = [(B.D.xT.D.)/ (B.D.-T.D.)]
= [(B.D.xT.D.)/B.G.]
T.D./B.G. = Sum/ B.D.
=1650/165
=10/1
Thus, if B.G. is Re 1, T.D. = Rs. 10.
If B.D.is Rs. ll, T.D.=Rs. 10.
If B.D. is Rs. 165, T.D. = Rs. [(10/11)xl65]
=Rs.150
And, B.G. = Rs. (165 - 150) = Rs. 15.
Sum = [(B.D.xT.D.)/ (B.D.-T.D.)]
= [(B.D.xT.D.)/B.G.]
T.D./B.G. = Sum/ B.D.
=1650/165
=10/1
Thus, if B.G. is Re 1, T.D. = Rs. 10.
If B.D.is Rs. ll, T.D.=Rs. 10.
If B.D. is Rs. 165, T.D. = Rs. [(10/11)xl65]
=Rs.150
And, B.G. = Rs. (165 - 150) = Rs. 15.
1411.What rate percent does a man get for his money when in discounting a bill due 10 months hence, he deducts 10% of the amount of the bill?
Bill: 13 1/3%
Bill: 12 1/3%
Bill: 10 1/3%
None of these
Explanation:
Let amount of the bill = Rs.100
Money deducted =Rs.10
Money received by the holder of the bill = Rs.100-10 = Rs.90
SI on Rs.90 for 10 months = Rs.10
Rate =[(100*10)/(90*10/12)%=13 1/3%
Let amount of the bill = Rs.100
Money deducted =Rs.10
Money received by the holder of the bill = Rs.100-10 = Rs.90
SI on Rs.90 for 10 months = Rs.10
Rate =[(100*10)/(90*10/12)%=13 1/3%
2505.The bankers discount on a certain sum due 2 years hence is $\dfrac{11}{10}$ of the true discount.The rate percent is:
11%
10%
5%
5.5%
Explanation:
Let T.D. be Re. 1.
| Then, B.D. = Rs.$ \dfrac{11}{10} $= Rs. 1.10. |
| $\therefore$ Sum = Rs.$ \left(\dfrac{1.10 \times 1}{1.10 - 1} \right) $= Rs.$ \left(\dfrac{110}{10} \right) $= Rs. 11. |
$\therefore$ S.I. on Rs. 11 for 2 years is Rs. 1.10
| $\therefore$ Rate =$ \left(\dfrac{100 \times 1.10}{11 \times 2} \right) $%= 5%. |
2510.The present worth of a certain sum due sometime hence is Rs. 3400 and the true discount is Rs. 340. The bankers gain is:
Rs. 21
Rs. 17
Rs. 18
Rs. 34
Explanation:
$BG =\dfrac{{TD}^2 }{PW} = \dfrac{{340}^2 }{3400}$
$= \dfrac{340 \times 340 }{3400} = \dfrac{340}{10} = Rs.34$
2511.The present worth of a certain bill due sometime hence is Rs. 1296 and the true discount is Rs. 72. What is the bankers discount?
Rs. 76
Rs. 72
Rs. 74
Rs. 4
Explanation:
$BG = \dfrac{{TD}^2 }{PW} = \dfrac{{72}^2}{1296}$
= $\dfrac{72 \times 72}{1296} = \dfrac{12 \times 12}{36} = \dfrac{12}{3} =Rs.4$
BG = BD - TD
=> 4 = BD - 72
=> BD = 72 + 4 = Rs. 76
2512.The bankers gain on a sum due 3 years hence at 12% per annum is Rs. 360. The bankers discount is:
Rs. 1360
Rs. 1000
Rs. 360
Rs. 640
Explanation:
BG = Rs. 360
T = 3 years
R = 12%
$TD =\dfrac{BG\times 100}{TR}$
$= \dfrac{360 \times 100}{3 \times 12} = Rs. 1000$
BG = BD - TD
=> BD = BG + TD = 360 + 1000 = Rs. 1360
2513.The bankers discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:
Rs. 400
Rs. 360
Rs. 480
Rs. 320
Explanation:
T.D =$ \frac{B.D\times100}{100\left(R\times T\right)}$
= Rs.$\left[\frac{420\times100}{100+\left(15\times1/3\right)}\right]$
=$\left[\frac{420\times100}{105}\right]$
= Rs. 400.
2514.The bankers gain on a bill due 1 year hence at 12% per annum is Rs. 6. The true discount is:
Rs. 72
Rs. 36
Rs. 54
Rs. 50
Explanation:
| T.D. =$ \dfrac{B.G. \times 100}{R \times T} $= Rs.$ \left(\dfrac{6 \times 100}{12 \times 1} \right) $= Rs. 50. |
2515.The present worth of a sum due sometime hence is Rs. 576 and the bankers gain is Rs. 16. The true discount is:
Rs. 36
Rs. 72
Rs. 48
Rs. 96
Explanation:
T.D. = $ \sqrt{P.W. \times B.G.} $ = $ \sqrt{576 \times 16} $ = 96.
2516.The certain worth of a certain sum due sometime hence is Rs. 1600 and the true discount is Rs. 160. The bankers gain is:
Rs. 20
Rs. 24
Rs. 16
Rs. 12
Explanation:
| B.G. =$ \dfrac{(T.D.)^2}{P.W.} $= Rs.$ \left(\dfrac{160 \times 160}{1600} \right) $= Rs. 16. |