# Railway Exam Arithmetic – Simple Interest & Compound Interest

Dear Readers, Here we have given from Aptitude Questions for Railway Exam. Candidates those who are all preparing for these exams can use this material.
1).What will be the difference between SI and CI on a sum of Rs.1500 for two years at the same rate of interest of 12(1/2) % per annum?
a)  Rs.234.375
b)  Rs.230.550
c)  Rs.250.129
d)  Rs.324.357
2).The simple interest on a sum for 5 yr is one-fourth of the sum. The rate of interest per annum is
a)  5%
b)  6%
c)  4%
d)  8%
3).If the simple interest on a certain sum of money for 3 yr is Rs.225 and the compound interest on the same sum at the same rate for 2 yr is Rs.153, then the principle invested (in Rs) is
a)  3000
b)  1875
c)  1500
d)  2250
4). The compound interest on Rs 30000 at 7% per annum for a certain time is Rs.4347. The time is?
a)  2 yr
b)  2.5 yr
c)  3 yr
d)  4 yr
5).A and B deposited together Rs.2000 in a bank at a rate of 5%. After 3 and 4 yr, A and B get equal amounts. whatis the share of A ?
a)  Rs 1034
b)  Rs 1054
c)  Rs 1084
d)  Rs 1024
6).A tape recorder is sold for Rs 3500 cash, or Rs 1000 cash down payment and the balance in three equal easy installments. If 12(1/2)% is the rate of interest compounded annually, find the amount of installment.
a)  Rs 1050.65
b)  Rs.1049.83
c)  Rs.1000.35
d)  Rs.1100.45
7).If the compound interest on a certain sum for two consecutive years is Rs 220 and Rs 242, then the rate of interest per annum is
a)  8%
b)  10%
c)  11%
d)  12%
8).If the amount is 2.25 times of the sum after 2 yr at compound interest (Compound annually), the rate of interest per annum is
a)  25%
b)  30%
c)  45%
d)  50%
9).A person borrows Rs.5000 for 2yr at 4% per annum single interest. He immediately lends to another person at 6 (1/4)% per annum for 2 yr. His gain in the transaction per year is
a)  Rs 112.50
b)  Rs 450.00
c)  Rs 244.53
d)  Rs 150.00
10).A, B and C enter into a partnership. A initially invests Rs 25 Lac and adds another Rs 10 Lac after one year B initially invests Rs 35 Lac and withdraws Rs 10 Lac after 2 yr and C invests Rs 30 Lac. In what ratio should the profits be divided at the end of three years?
a)  20 : 19 : 18
b)  10 : 10 : 9
c)  20 : 20 : 19
d)  19 : 19 :18
1). a)  2). a)  3). b)  4). a)  5). d)  6). b)  7). b)  8). d)  9). a)  10). d)
Detailed Explanation:
1). :. Required difference
=15000(25 / [2 * 100])2 =15000 / 64
= Rs 234.375
2). Simple interest = [principle * Rate * Time] / 100
:. X / 4 = [x * r * 5] / 100
➾ r = 100 / [4 * 50]
➾ r = 5 %
3). Let the principle be Rs P.
Rate of interest = R%
Using formula of simple interest SI = [P * R * T] / 100
225 = [P * R * 3] / 100
[225 * 100] / 3 = P * R
P * 7500 ➾R = 7500 / P
Now, using formula of Amount for Compound Interest
CI = P[(1 +(R / 100))2 – 1]
Putting value of CI and R calculated above
153 = P [(1 + (7500/ P * 100))2 – 1 ]
[153 / P] + 1= [(P + 75) / P] 2
[153 + P] / P = [(P + 75)2 / P2] P
(153 +P) = P2 + 150P + 5625
153P + P2 = P2+ 150 P + 5625
153P – 150P = 5625
3P = 5625
P = 5625 / 3
= Rs 1875
4). P = 3000
R = 7%
CI=4347
T=?
Using  formula for compound interest
CI = P [( 1 +(R /100))T – 1 ]
➾4347 = 3000[1 + (7 / 100)T – 1]
➾[4347 / 30000] + 1= (107 / 100)T
➾(30000 + 4347)/ 30000 =[107 / 100]T
➾34347 / 30000 =(107 /100)T
➾11449 / 10000 =(107 / 100)T
➾(107 * 107) / (100 * 100) = (107 / 100)T
➾(107 / 100)2 =(107 / 100)T
:. T = 2 yr
5). Let A’s share be Rs X.
:. B’s share = Rs (2000 – X), then
Given,
X [1 + (5 / 100)]3 = (2000 – X) [1 + ( 5 / 100)]4
➾ X = (2000 – X)(21 / 20)
➾ 20X = 2000 * 21 – 21X
:. X = 42000 / (20 + 21) = 42000 / 41
= 1024.339 ≈Rs. 1024
6). Let each installment be Rs X
Amount = 3500 – 1000 = Rs 25000
:. X / [1 + (25 / 200)] + X / [1 + (25 / 200)]2 + X / [1 + (25 / 200)]3 =2500
➾[8 / 9]X + [8 / 9]2 X+ [8 / 9]3 X = 2500
➾ 8 / 9 X[1 + (8 / 9) +(64 / 81)] = 2500
➾  8 / 9[(81 + 72 + 64) / 81] = 2500
➾ 8 / 9 X * 217 / 81 = 2500
:. X = (2500 * 9 * 81) / 8 * 217 = Rs 1049.83
7). Let the principle be Rs P and Interest be r%
According to question,
Interest for a consecutive year is Rs 242.
:. Interest on Rs 220 is Rs (242 – 220) i.e., Rs 22.
:. 22 = (220 * 1 * r) / 100
➾ r =(2200 / 220) = 10%
8). Let the principle be Rs. P and the rate of interest = 1%
According to question, A = 2.25 P, n =  2yr
:. 2.25 P = P[ 1 +( r / 100)]2
➾ 2.25 = [1 + (r / 100)]2
➾1.5 = 1+ (r / 100)
➾ r / 100 = 0.5
➾r = 50%
9). Principle = Rs.5000,
t = 2 yr, r1 = 4%, r2 = 6(1 / 4)%
:. Gain = [5000 * 9 *2] / [100 * 4] = 225
➾Gain per year =225 / 2
= Rs 112.50
10). Ratio of their investment
= ([2500000 * 1] + [3500000 * 2] ) : ([3500000 * 2]  + [2500000 * 1]) : (3000000 * 3)
=9500000 : 9500000 : 9000000
= 19 : 19 : 18 