Home ≫ Arithmetic Aptitute ≫ SimpleInterest ≫ Page 4
31. Rs 1,200 amounts to Rs 1,632 in 4 years at a certain rate of simple interest. If the rate of interest is increased by 1%, it would amount to how much?
  A.  Rs 1730
  B.  Rs 1680
  C.  Rs 1700
  D.  Rs 1650
     
   
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 = 1200, A = 1632, r = 1, t1 = 4, t2 = 4
Using these values in shortcut, we get:
=
[
(
1632 − 1200 / 4
)
+
(
1 x 1200 / 100
)
]
4
=
[
432 / 4
+ 12
]
4 = (108 + 12) x 4 = 480
∴ New Amount = Rs (1200 + 480) = Rs 1680

32. The simple interest on a sum of money will be Rs 600 after 5 years. In the next 5 years principal is triple, what will be the total interest at the end of the 10th year?
  A.  Rs 2400
  B.  Rs 2280
  C.  Rs 2580
  D.  Rs 2100
     
   
View Answer

Shortcut:
The simple interest on a sum of money will be Rs z after t years. If in the next 't' years principal becomes a times, then the total interest at the end of the '2t'th year is given by Rs [(a+1)z]
Here, z = 600, t1 = 5, t2 = 5, a = 3 (triple times)
Using these values in shortcut, we get:
= [(3 + 1)600] = 2400
∴ Required S.I = Rs 2400

33. The simple interest on a sum of money will be Rs 600 after 4 years. In the next 6 years principal becomes 4 times, what will be the total interest at the end of the 10th year?
  A.  Rs 3900
  B.  Rs 4410
  C.  Rs 4120
  D.  Rs 4200
     
   
View Answer

Shortcut:
The simple interest on a sum of money will be Rs z after t1 year. If in the next t2 years principal becomes a times, then the total interestat the end of (t1 + t2)th years is given by Rs z
[
1 +
(
t2 / t1
)
a
]

Here, z = 600, t1 = 4, t2 = 6, a = 4
Using these values in shortcut, we get:
= 600
[
1 +
(
6 / 4
)
4
]
= 600[1 + 6] = 4200
∴ Total simple interest after 10 years = Rs 4200.

34. A sum of Rs 7800 is lent out in two parts in such a way that the interest on one part at 10% for 5 years is equal to that on another part at 9% for 6 years. Find the two sums.
  A.  First part: Rs 1650; Second part: Rs 6150
  B.  First part: Rs 1800; Second part: Rs 6200
  C.  First part: Rs 4050; Second part: Rs 3750
  D.  First part: Rs 5050; Second part: Rs 2750
     
   
View Answer

Shortcut:
A sum of Rs Z is lent out in n parts in such a way that the interest on first part at r1% for t1 years, the interest on second part at r2% for t2 years the interest on third part at r3% for t3 years, and so on, are equal, the ratio in which the sum was divided in n parts is given by
1 / r1 x t1
:
1 / r2 x t2
:
1 / r3 x t3
..........
1 / rn x tn

Here, Z = 7800, r1 = 10, t1 = 5, r2 = 9, t2 = 6
Using these values in shortcut, we get:
S1 : S2 =
1 / 10 x 5
:
1 / 9 x 6
=
1 / 50
:
1 / 54
= 54 : 50 = 27 : 25
∴ First part =
27 / 52
x 7800 = Rs 4050
Second part = 7800 − 4050 = Rs 3750

35. An amount of money becomes four times at the simple interest rate of 5% per annum. At what rate per cent will it become ten times?
  A.  20%
  B.  15%
  C.  22%
  D.  25%
     
   
View Answer

Shortcut:
if a sum of money becomes 'a' times at the simple interest rate of r% per annum, then it will become 'b' times at the simple interest rate of
[
(
b − 1 / a − 1
)
x r]%
Here, a = 4, r = 5, b = 10
Using these values in shortcut, we get:
Required rate =
[
(
10 − 1 / 4 − 1
)
x 5
]
% =
[
(
9 / 3
)
x 5
]
% = 15%

36. A certain sum of money amounted to Rs 600 at 5% in a time in which Rs 750 amounted to Rs 870 at 4%. If the rate of interest is simple, find the sum.
  A.  Rs 530
  B.  Rs 480
  C.  Rs 500
  D.  Rs 610
     
   
View Answer

Shortcut:
A certain sum of money amounted to Rs Z1 at r1% in a time in which Rs Q amounted to Rs Z2 at r2%. If the rate of interest is simple, then the sum is given by Rs
[
Z1 / (1 − r1/r2) + {(Z2 x r1)/(Q x r2)}
]

Here, Z1 = 600, r1 = 5, Q = 750, Z2 = 870, r2 = 4
Using these values in shortcut, we get:
Required sum =
[
600 / (1 − 5/4) + {(870 x 5)/(750 x 4)}
]
=
[
600 / (− 1/4) + {(87)/15 x 4}
]
=
[
600 / (− 0.25 + 1.45
]
=
[
600 / 1.2
]
= 500
Hence, the sum is Rs 500.

37. A sum of money amounts to Rs 2600 in 6 years at 5% per annum. In how many years will it amount to Rs 4000 at the same rate?
  A.  25 years
  B.  15 years
  C.  10 years
  D.  20 years
     
   
View Answer

Shortcut:
A certain sum of money amounts to Rs Z1 in t years at r% per annum, then the time in which it will amount to Rs Z2 at the same rate of interest is given by
[
Z2 / Z1
(
t +
100 / r
)
−
100 / r
]
years.
Here, Z1 = 2600, t = 6, r = 5, t2 = ?, Z2 = 4000
Using these values in shortcut, we get:
Required time =
[
4000 / 2600
(
6 +
100 / 5
)
−
100 / 5
]
=
[
20 / 13
(6 + 20) − 20
]
=
[
(
20 / 13
)
26 − 20
]
= 40 − 20 = 20
Hence, the time will be 20 years.

38. Ajit invests an amount of Rs 15,000 in the name of his three sons X, Y, and Z in such a way that they get the same amount after 2, 3 and 4 years respectively. If the rate of simple interest is 5% then find the ratio in which the amount was invested for X, Y and Z.
  A.  253:264:276
  B.  276:264:253
  C.  264:276:253
  D.  270:261:249
     
   
View Answer

Shortcut:
When different amounts mature to the same amount at simple rate of interest, the ratio of the amounts invested are in inverse ratio of (10 + time x rate). That is the ratio in which the amounts are invested is
1 / 100 + r1t1
:
1 / 100+ r2t2
:
1 / 100 + r3t3
............ :
1 / 100 + rntn

Here, t1 = 2, t2 = 3, t3 = 4, r1 = 5, r2 = 5, r3 = 5
Using these values in shortcut, we get:
Required ratio =
1 / 100 + 5 x 2
:
1 / 100 + 5 x 3
:
1 / 100 + 5 x 4
=
1 / 100 + 10
:
1 / 100 + 15
:
1 / 100 + 20
=
1 / 110
:
1 / 115
:
1 / 120
=
1 / 22
:
1 / 23
:
1 / 24
=
276 : 264 : 253 / 6072
= 276 : 264 : 253
Hence, the ratio will be 276 : 264 : 253.

39. A certain sum of money amounts to Rs 2600 in 6 years at 5% per annum, Find the sum.
  A.  Rs 2000
  B.  Rs 2500
  C.  Rs 1600
  D.  Rs 2200
     
   
View Answer

Shortcut:
The direct relationship between the principal(P) and the amount (A) and is given by sum
100 x A / 100 + rt

Here, A = 2600, r = 5, t = 6
Using these values in shortcut, we get:
Required sum =
100 x 2600 / 100 + 5 x 6
=
100 x 2600 / 100 + 30
=
100 x 2600 / 130
= 100 x 20 = 2000
Hence, the sum is Rs 2000.

40. Ajit lent a certain sum of money at 5% simple interest and in 8 years the interest amounted to Rs 300 less than the sum lent. Find the sum lent.
  A.  Rs 475
  B.  Rs 510
  C.  Rs 500
  D.  Rs 630
     
   
View Answer

Shortcut:
A person lent a certain sum of money at r% simple interest and in 't' years the interest amounted to Rs Z less than the sum lent, then the sum lent is given by Rs
100 x Z / 100 − rt

Here, Z = 300, r = 5, t = 8
Using these values in shortcut, we get:
Required sum =
100 x 300 / 100 − 5 x 8
=
100 x 300 / 100 − 40
=
100 x 300 / 60
= 100 x 5 = 500
Hence, the sum is Rs 500.

Copyright © 2020-2022. All rights reserved. Designed, Developed and content provided by Anjula Graphics & Web Desigining .