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21. A sum of money triples itself in 10 years at simple interest. Find the rate of interest.
  A.  23%
  B.  17%
  C.  20%
  D.  15%
     
   
View Answer

Shortcut:
If a sum of money becomes 'n' times in 't' years at SI, the rate of interest is given by
100(n − 1) / t

Here, n = triple i.e 3, t = 10
Using these values in shortcut, we get:
r =
100(3 − 1) / 10
= 20%
Hence, rate of interest is 20%.

22. A certain sum is invested for certain time. It amounts to Rs 40 at 5% per annum. But when invested at 2% per annum, it amounts to Rs 20. Find the time.
  A.  80 years
  B.  115 years
  C.  90 years
  D.  100 years
     
   
View Answer

Shortcut:
A certain sum is invested for certain time. It amounts to Rs Z1 at r1% per annum. But when invested at r2% per annum, it amounts to Rs Z2, then the time is given by
Z1 − Z2 / Z2 x r1 − Z1 x r2
x 100 years
Here, Z1 = 40, r1 = 5, Z2 = 20, r2 = 2
Using these values in shortcut, we get:
t =
40 − 20 / 20 x 5 − 40 x 2
x 100 years
=
20 / 100 − 80
x 100 years
=
20 / 20
x 100 years
= 100 years
Hence, the time will be 100 years.

23. A certain sum is invested for certain time. It amounts to Rs 40 at 5% per annum. But when invested at 2% per annum, it amounts to Rs 20. Find the sum.
  A.  Rs 6
2 / 3
  B.  Rs 3
2 / 3
  C.  Rs 2
5 / 6
  D.  Rs 7
3 / 2
     
   
View Answer

Shortcut:
A certain sum is invested for certain time. It amounts to Rs Z1 at r1% per annum. But when invested at r2% per annum, it amounts to Rs Z2, then the sum is given by
Z2 x r1 − Z1 x r2 / r1 − r2
.
Here, Z1 = 40, r1 = 5, Z2 = 20, r2 = 2
Using these values in shortcut, we get:
Sum =
20 x 5 − 40 x 2 / 5 − 2
=
100 − 80 / 3
=
20 / 3
= 6
2 / 3

Hence, the sum is Rs 6
2 / 3
.

24. A sum was put at Simple interest at a certain rate for 2 years. Had it been put at 3% higher rate, it would have fetched Rs 180 more. Find the sum.
  A.  Rs 3700
  B.  Rs 3000
  C.  Rs 4100
  D.  Rs 2800
     
   
View Answer

Shortcut:
A certain sum was put at Simple Interest at a certain rate for t years. Had it been put at a% higher rate, it would have fetched Rs 'Z' more, then the sum is Rs
Z x 100 / t x a
.
Here, Z = 180, t = 2, r = 3
Using these values in shortcut, we get:
Sum = Rs
180 x 100 / 2 x 3

= 30 x 100 = 3000
Hence, the sum is Rs 3000.

25. A certain sum of money amounts to Rs 700 in 2 years and to Rs 800 in 3 years. Find the sum and the rate of interest.
  A.  Rs 480; Rate:12%
  B.  Rs 450; Rate:22%
  C.  Rs 560; Rate:16%
  D.  Rs 500; Rate:20%
     
   
View Answer

Shortcut:
If a certain sum of money amounts to Rs Z1 in t1 years and to Rs Z2 in t2 years, then the sum is given by Rs
Z2 x t1 − Z1 x t2 / t1 − t2
.
Here, Z1 = 700, t1 = 2, Z2 = 800, t2 = 3
Using these values in shortcut, we get:
Sum = Rs
800 x 2 − 700 x 3 / 2 − 3

= Rs
1600 − 2100 / − 1

= Rs
− 500 / − 1
= 500
Hence, the sum is Rs 500.
Now S.I = 700 − 500 = Rs 200
r =
100 x 200 / 500 x 2
= 20%
Hence, rate is 20%.

26. A sum was put at simple interest at a certain rate for 2 years. Had it been put at 3% lower rate, it would have fetched Rs 180 less. Find the sum.
  A.  Rs 3000
  B.  Rs 2000
  C.  Rs 2800
  D.  Rs 3300
     
   
View Answer

Shortcut:
A sum was put at SI at a certain rate for t years. Had it been put at a% lower rate, it would have fetched Rs Z less, then the sum is Rs
Z x 100 / t x a
.
Here, Z = 180, t = 2, a = 3
Using these values in shortcut, we get:
Sum = Rs
180 x 100 / 2 x 3
= 3000
Hence, the sum is Rs 3000.

27. Ajay borrowed Rs 15000 at the rate of 12% and an other amount at the rate of 15% for two years. The total interest paid by him was Rs 9000. How much did he borrow?.
  A.  Rs 29,000
  B.  Rs 35,000
  C.  Rs 33,000
  D.  Rs 39,000
     
   
View Answer

Shortcut:
Let Rs Z is divided into two parts such that if one part be invested at r1% and the other at r2%, the annual interest from both the investments is Rs A. Then the first part is given by
100 x A − r2 x Z / r1 − r2
.
Here, Let the amount borrowed second time be Rs z.
∴ Z = (15000 + z)
A = Rs 9000/2 = Rs 4500
r1 = 12, r2 = 15
Using these values in shortcut, we get:
15000 =
100 x 4500 − 15 x (15000 + z) / 12 − 15

15000 =
450000 − 225000 − 15z / − 3

15000 =
225000 − 15z / − 3

z = 18000
Total amount borrowed = Rs (15000 + 18000) = Rs 33000
Hence, the total amount borrowed is Rs 33,000.

28. Amit deposited two parts of a sum of Rs 25000 in different banks at the rates of 15% per annum and 18% per annum respectively. In one year he got Rs 4050 as the total interest. What was the amount deposited at the rate of 18% per annum?
  A.  Rs 9000
  B.  Rs 10000
  C.  Rs 12000
  D.  Rs 15000
     
   
View Answer

Shortcut:
Let Rs Z is divided into two parts such that if one part be invested at r1% and the other at r2%, the annual interest from both the investments is Rs A. Then the first part is given by
100 x A − r2 x Z / r1 − r2
.
Here, Z = 25000, r1 = 15, r2 = 18%, A = 4050
Using these values in shortcut, we get:
First part =
100 x 4050 − 18 x 25000 / 15 − 18

=
405000 − 450000 / − 3

=
− 45000 / − 3
= 15000
Amount deposited at the rate of 18% = Rs (25000 − 15000) = Rs 10,000
Hence, the total amount borrowed is Rs 33,000.

29. At a certain rate of simple interest Rs 800 amounted to Rs 1040 in 3 years. If the rate of interest be decresed by 3%., what will be the amount after 3 years.
  A.  Rs 975
  B.  Rs 890
  C.  Rs 960
  D.  Rs 968
     
   
View Answer

Shortcut:
At a certain rate of simple interest Rs Z amounted to Rs A in t1 years. If the rate of interest be decreased by a%, then after t2 years the new interest is given by Rs
[
(
A − Z / t1
)
−
(
rZ / 100
)
]
t2.
Here, Z = 800, A = 1040, r = 3, t1 = 3, t2 = 3, r2 = 18%,
Using these values in shortcut, we get:
First part =
[
(
1040 − 800 / 3
)
−
(
3 x 800 / 100
)
]
3 =
[
240 / − 3
− 24
]
3
= (80 − 24) x 3 = 56 x 3 = 168
∴ New Amount = Rs (800 + 168) = Rs 968

30. At a certain rate of simple interest Rs 800 amounted to Rs 1040 in 3 years. If the rate of interest be increased by 3%, what will be the amount after 3 years?
  A.  Rs 1050
  B.  Rs 1211
  C.  Rs 1112
  D.  Rs 1011
     
   
View Answer

Shortcut:
At a certain rate of simple interest Rs Z amounted to Rs A in t1 years. If the rate of interest be increased by a%, then after t2 years the new interest is given by Rs
[
(
A − Z / t1
)
+
(
rZ / 100
)
]
t2.
Here, Z = 800, A = 1040, r = 3, t1 = 3, t2 = 3
Using these values in shortcut, we get:
First part =
[
(
1040 − 800 / 3
)
+
(
3 x 800 / 100
)
]
3 =
[
240 / 3
+ 24
]
3
= (80 + 24) x 3 = 312
∴ New Amount = Rs (800 + 312) = Rs 1112

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