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11. Find the true discount rekoning 4 per cent per annum simple interest of Rs 481.25 due in 2
1 / 2
years time.
  A.   41.75
  B.   43.75
  C.   42.50
  D.   43.20
     
   
View Answer

Shortcut:
To find true discount when rate, amount/sum and time are given.
True Discount (TD) =
A x R x T / 100 + RT

where A = Amount, R = rate and T = time
Here, A = 481.25, R = 4, T = 2
1 / 2
=
5 / 2

Using these values in the shortcut, we get:
True Discount (TD) =
481.25 x 4 x 5/2 / 100 + (4 x 5/2)

=
481.25 x 10 / 100 + 10

=
4812.5 / 110
= 43.75
Hence, the true discount is Rs 43.75.
[Note: True discount can be found by first calculting present worth and then subtracting it form the sum or amount.]

12. If the true discount on a sum due 2 years hence at 5% per annum be Rs 75, then the sum due is:
  A.   825
  B.   810
  C.   830
  D.   840
     
   
View Answer

Shortcut:
To find true discount when rate, amount/sum and time are given.
True Discount (TD) =
A x R x T / 100 + RT

where A = Amount, R = rate and T = time
Here, A = ?, R = 5, T = 2, T.D = 75
Using these values in the shortcut, we get:
True Discount (TD) =
A x 5 x 2 / 100 + (5 x 2)

75 =
10 x A / 110

75 x 110 = 10 x A
A = 75 x 11 = 825
Hence, the amount is Rs 825.

13. Find the true discount on a bill for Rs 1270 due 7 months hence at 10% per annum.
  A.   75
  B.   80
  C.   60
  D.   70
     
   
View Answer

Shortcut:
To find true discount when rate, amount/sum and time are given.
True Discount (TD) =
A x R x T / 100 + RT

where A = Amount, R = rate and T = time
Here, A = 1270, R = 10, T =
7 / 12

Using these values in the shortcut, we get:
True Discount (TD) =
1270 x 10 x 7/12 / 100 + (10 x 7/12)

=
1270 x 10 x 7/12 / 100 + 70/12

=
1270 x 10 x 7/12 / (1200 + 70)/12

=
1270 x 10 x 7 / 1270
= 70
Hence, the true discount is Rs 70.

14. The true discount on a bill due 9 months hence at 12% per annum is Rs 270. Find the present worth.
  A.   Rs. 2800
  B.   Rs. 2500
  C.   Rs. 3000
  D.   Rs. 3200
     
   
View Answer

Shortcut:
To find Present Worth (PW), when True Discount (TD), rate (R) and time (T) are given.
Present Worth (PW) =
100 x T.D / R x T

Here, TD = 270, R = 12, T =
9 / 12

Using these values in the shortcut, we get:
PW =
100 x 270 / 12 x 9/12

=
100 x 270 / 9
= 3000
Hence, the present value is Rs 3000.

15. The true discount on a bill due 8 months hence at 12 % per annum is Rs 240.Find the amount of the bill and its present worth.
  A.   Rs 3100,Rs. 3340
  B.   Rs 3000,Rs. 3240
  C.   Rs 3500,Rs. 3440
  D.   Rs 3240,Rs. 3220
     
   
View Answer

Shortcut:
To find Present Worth (PW), when True Discount (TD), rate (R) and time (T) are given.
Present Worth (PW) =
100 x T.D / R x T

Here, TD = 240, R = 12, T =
8 / 12

Using these values in the shortcut, we get:
PW =
100 x 240 / 12 x 8/12

=
100 x 240 / 8
= 3000
∴ The present value is Rs 3000.
Hence, Amount = PW + TD = 3000 + 240 = 3240

16. The interest on Rs. 750 for 2 years is equal to the true discount n Rs 810 for the same time and at the same rate. The rate per cent is :
  A.  2 %
  B.  6 %
  C.  4 %
  D.  5 %
     
   
View Answer

Shortcut:
To find Present Worth (PW), when True Discount (TD), rate (R) and time (T) are given.
Present Worth (PW) =
100 x T.D / R x T

Here, We know that TD is SI on PW,
So, S.I = 810 − 750 = 60 on Rs 750 for 2 years.
PW = 750, R = ?, T = 2, SI = 60
R =
100 x 60 / 750 x 2

=
100 / 25
= 4

∴ The rate is 4%.

17. Goods were bought for Rs.600 and sold and the same day for Rs 650.25 at a credit of 9 months and still there was a gain of 2%. The rate per cent is:
  A.  7
2 / 5
%
  B.  8
5 / 3
%
  C.  5
3 / 8
%
  D.  8
1 / 3
%
     
   
View Answer

Shortcut:
To find Present Worth (PW), when True Discount (TD), rate (R) and time (T) are given.
Present Worth (PW) =
100 x T.D / R x T

Here, S.P = 102% of 600 = 612
∴ PW of Rs 650.25 due 9 months hence is Rs 612
or, Rs 38.25 is SI on Rs 612 for 9 months.
PW = 612, R = ?, T =
9 / 12
, SI = 38.25
R =
100 x 38.25 / 612 x 9/12

=
3825 / 459
= 8
1 / 3


∴ The rate is 8
1 / 3
%.

18. The true discount on a bill due 2 years hence at 5% per annum is Rs 15.Find the amount of the bill.
  A.   Rs 150
  B.   Rs 165
  C.   Rs 178
  D.   Rs 170
     
   
View Answer

Shortcut:
To find Amount (A), when True Discount (TD), rate (R) and time (T) are given.
A = TD[1 +
100 / R x T
]
Here, TD = 15, R = 5, T = 2
A = 15[1 +
100 / 5 x 2
]
= 15[1 + 10] = 15 x 11 = 165

19. The true discount on a bill due 3
1 / 2
years hence at 3
1 / 2
% per annum is Rs 24.50. Find the amount of the bill.
  A.   Rs224.50
  B.   Rs226.50
  C.   Rs220.25
  D.   Rs225.50
     
   
View Answer

Shortcut:
To find Amount (A), when True Discount (TD), rate (R) and time (T) are given.
A = TD[1 +
100 / R x T
]
Here, TD = 24.5, R =
7 / 2
, T =
7 / 2

A = 24.5[1 +
100 / 7/2 x 7/2
]
= 24.5[1 +
100 x 4 / 49
]
= 24.5[1 +
400 / 49
]
= 24.5 x
49 + 400 / 49

= 24.5 x
449 / 49
= 224.5
Hence, the amount on the bill is Rs 224.50.

20. Find the difference between simple interest and true discount on Rs 840 due 4 years hence at 5% per annum simple interest.
  A.   Rs 30
  B.   Rs 25
  C.   Rs 28
  D.   Rs 26
     
   
View Answer

Shortcut:
To find the difference between simple interest (SI) and True Discount (TD), when amount (A), rate (R) and time (T) are given.
SI − TD =
A x (RT)2 / 100(100 + RT)
]
Here, A = 840, R = 5, T = 4
Using these values in the shortcut, we get:
SI − TD =
840 x (5 x 4)2 / 100(100 + 5x4)
]
=
840 x 20 x 20 / 100(100 + 20)
]
=
840 x 20 x 20 / 100 x 120
] = 28
Hence, the difference is Rs 28.

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