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21. Find the difference between simple interest and true discount on Rs 960 due 4 years hence at 5% per annum simple interest.
  A.  Rs 28
  B.  Rs 30
  C.  Rs 32
  D.  Rs 35
     
   
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 = 960, R = 5, T = 4
Using these values in the shortcut, we get:
SI − TD =
960 x (5 x 4)2 / 100(100 + 5 x 4)
]
=
960 x 20 x 20 / 100(100 + 20)

=
960 x 20 x 20 / 100 x 120
= 32
Hence, the difference is Rs 32.

22. The difference between the simple interest and the true discount on a certain sum for 6 months at 4 % is Rs. 15.Find the sum.
  A.   Rs. 39,210
  B.   Rs. 39,200
  C.   Rs. 38,150
  D.   Rs. 38,250
     
   
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 = ?, R = 4, T =
1 / 2
, SI − TD = 15
Using these values in the shortcut, we get:
SI − TD =
A x (4 x 1/2)2 / 100(100 + 4 x 1/2)
]
15 =
A x 2 x 2 / 100 x 102

15 x 100 x 102 = A x 4
A =
15 x 100 x 102 / 4
= 15 x 25 x 102 = 38250
Hence, the amount is Rs 38250.

23. The true discount on a certain sum of money due after 2
1 / 2
years at 6 % per annum is less than the simple interest on the same sum for the same time by Rs 81. Find the sum.
  A.   Rs.4140
  B.   Rs.4240
  C.   Rs.4180
  D.   Rs.4060
     
   
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 = ?, R = 6, T = 2
1 / 2
=
5 / 2
, SI − TD = 81
Using these values in the shortcut, we get:
SI − TD =
A x (6 x 5/2)2 / 100(100 + 6 x 5/2)
]
81 =
A x 15 x 15 / 100 x 115

81 x 100 x 115 = A x 225
A =
81 x 100 x 115 / 225
= 9 x 4 x 115 = 4140
Hence, the amount is Rs 4140.

24. The true discount on Rs 2040 due after a certain time at 6% per annum is Rs 40. Find the time after which it is due.
  A.  1 month
  B.  4 months
  C.  3 months
  D.  5 months
     
   
View Answer

Shortcut:
To find the time when True Discount (TD), amount (A) and rate (R) are given. T =
100 x TD / (A − TD) x R

Here, A = 2040, R = 6, TD = 40
Using these values in the shortcut, we get:
T =
100 x 40 / (2040 − 40) x 6

=
4000 / 2000 x 6

=
1 / 3

Hence, the time is
1 / 3
years or 4 months.

25. The true discount on Rs 260 due 3 years hence is Rs 60. Find the rate per cent.
  A.   11%
  B.   8%
  C.   5%
  D.   10%
     
   
View Answer

Shortcut:
To find the rate (R) when True Discount (TD), amount (A) and time (T) are given. R =
100 x TD / (A − TD) x T

Here, A = 260, R = ?, TD = 60, T = 3
Using these values in the shortcut, we get:
R =
100 x 60 / (260 − 60) x 3

=
100 x 60 / 200 x 3
= 10
Hence, the rate is 10%.

26. The true discount on Rs 1,860 due 2 years hence is Rs 60. Find the rate per cent
  A.   1.67%
  B.  2.6%
  C.   3.5%
  D.   1.25%
     
   
View Answer

Shortcut:
To find the rate (R) when True Discount (TD), amount (A) and time (T) are given. R =
100 x TD / (A − TD) x T

Here, A = 1860, R = ?, TD = 60, T = 2
Using these values in the shortcut, we get:
R =
100 x 60 / (1860 − 60) x 2

=
100 x 60 / 1800 x 2
=
5 / 3
= 1.67
Hence, the rate is 1.67%.

27. If the true discount on Rs 161 due 2 ½ years hence be Rs 21, at what rate per cent is the interest calculated?
  A.  7%
  B.  4%
  C.  6%
  D.  5%
     
   
View Answer

Shortcut:
To find the rate (R) when True Discount (TD), amount (A) and time (T) are given. R =
100 x TD / (A − TD) x T

Here, A = 161, R = ?, TD = 21, T = 5/2
Using these values in the shortcut, we get:
R =
100 x 21 / (161 − 21) x 5/2

=
100 x 21 / 140 x 5/2
=
2100 / 350
= 6
Hence, the rate is 6%.

28. What must be the rate of interest in order that the discount on Rs 774.76 payable at the end of 3 years may be Rs. 83.01%?
  A.  7%
  B.  4%
  C.  5%
  D.  3%
     
   
View Answer

Shortcut:
To find the rate (R) when True Discount (TD), amount (A) and time (T) are given. R =
100 x TD / (A − TD) x T

Here, A = 774.76, R = ?, TD = 83.01, T = 3
Using these values in the shortcut, we get:
R =
100 x 83.01 / (774.76 − 83.01) x 3

=
8301 / 691.75 x 3
= 4
Hence, the rate is 4%.

29. The true discount on a certain sum of money due 6 years hence is Rs 200 and the simple interest on the same sum for the same time and at the same rate is Rs 300. Find the sum.
  A.   Rs 610
  B.  Rs 580
  C.   Rs 500
  D.   Rs 600
     
   
View Answer

Shortcut:
To find the sum/amount (A) when simple interest (SI) and True Discount (TD) are given. Sum or Amount (A) =
SI x TD / SI − TD

Here, SI = 300, TD = 200
Using these values in the shortcut, we get:
Sum or Amount (A) =
300 x 200 / 300 − 200

=
300 x 200 / 100
= 600
Hence, the sum is Rs 600.

30. The true discount on a certain of money due 3 years hence is Rs 100 and the simple interest on the same sum for the same time and at the same rate is Rs 120. Find the sum and the rate per cent.
  A.   Rs560,7
3 / 4
  B.   Rs600,3
2 / 5
  C.   Rs600,6
2 / 3
  D.   Rs620,5
3 / 4
     
   
View Answer

Shortcut:
To find the sum/amount (A) when simple interest (SI) and True Discount (TD) are given. Sum or Amount (A) =
SI x TD / SI − TD

Here, SI = 120, TD = 100
Using these values in the shortcut, we get:
Sum or Amount (A) =
120 x 100 / 120 − 100

=
120 x 100 / 20
= 600
Hence, the sum is Rs 600.
Rate =
100 x 120 / 600 x 3
=
20 / 3
= 6
2 / 3

Hence, the rate is 6
2 / 3
%.

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