# Arithmetic Reasoning: Solved Examples

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All the important and typical questions related to arithmetic reasoning are covered in this article. We strongly recommend that the reader should first attempt to solve the problem on his own and only then look at the solution here.
1. In a college, there are 34 girls who have car. If these constitute one fifth of the girls and the total no. of girls is two-fifth of the total no. of students in the college, what is the no. of boys in the college?
A. 425
B. 220
C. 185
D. 255
Let the number of girls be x. So, (1/5) x = 34 or x = 34 x (5/1) = 170.
If total no. of students is y, then (2/5) y = 170 or y = 170 x (5/2) = 425.
Therefore, Number of boys in the college = (425 - 170) = 255
2. Joseph is now 1/4th times as old as his mother Ketty. Four years hence, his mother will be three times as old as her son. The age of his mother Ketty (in years) is
A. 32
B. 35
C. 8
D. 24
Let Joseph’s mother Ketty age be 4x years. Then, Joseph’s age = x years.
Four years hence, Joseph's age = (x + 4) years and Joseph’s mother Ketty age = (4x + 4) years.
So, 4x+4= 3 (x+4)
4x-3x= 12-4;
x = 8.
Joseph's mother Ketty age = 4x= 4 x 8=32 years
3. A director's total salary is sum of his rent charges, deposits and expenditure. During one month his deposits is equal to expenditure which is 2/3 of rental charges. What fraction of his total income saves in deposits?
A. 4/9
B. 5/4
C. 5/8
D. 2/7
Let Rent charges= Rs.x,
Deposits = Expenditure= Rs. 2/3 x
Salary =Rental Charges+ Deposits + Expenditure
= x + (2/3)x + (2/3)x = (7/3)x
Required Fraction = (2x / 3) x (3/7x) = 2/7
1. Rina & Rohit are playing a game, Rina writes down all the natural numbers from 1 to 100, then Rohit has to calculate how many times does she write four?
A. 11
B. 18
C. 20
D. 21
From 1 to 100, there are exactly 10 numbers with 4 as their tens digit – 40, 41, 42 ,43 ,44, 45,46,47,48,49 ; and 10 numbers with 4 as their unit digit: 4,14,24,34,44, 54,64,74,84,94
So, the required number of numbers = 10 + 10 = 20
2. At Anoop’s Birthday party, there are exactly 57 persons including Anoop. They shake hand with each other.  Find the total number of handshakes.
A. 1956
B. 1599
C. 1965
D. 1596
1st person shakes hand with 56 persons,
2nd person shakes hand with 55 persons because he already shakes hand with the 1st person.
And 3rd person shakes hand with 54 and so on.
Therefore, total number of  handshakes = 56+55+54+…….+3+2+1
= 1+2+3+…………….+54+55+56
Formula for sum of Natural numbers= n(n+1) / 2
Total number of  hand shakes = Sum of 56 natural numbers= 56(56+1) / 2 = 56x57/2 = 1596
3. Four tubelights begin to light together and light at intervals of 5, 8, 9 and 11 seconds respectively. How many times will they light together in two hours including the one at the start?
A. 2 times
B. 3 times
C. 4 times
D. 5 times
L.C.M. of 5, 8, 9 & 11 is 3960.
So, the tubelights will light together after every 3960 seconds i.e. 1 hour 6 minutes.
Therefore, in two-hours (or 120 minutes), the tubelights will light together 2 times, including the one at the start.
4. An airplane starts from country X. The no. of males in the airplane is thrice of the no. of females. In country Y, six females enter and 10 males leave the airplane at country W. Now, no. of males & females is equal. How many persons entered in the airplane from the beginning?
A. 15
B. 30
C. 36
D. 32
Originally, let number of females = x. Then, number of males = 3x.
So, in city Y, we have: (3x - 10) = (x + 6) or x =8.
Therefore Total number of persons in the beginning = (x + 3x) = 4x = 32
5. There are four friends Amit, Ram, Rohit and Kirti. In an examination, the sum of their marks is 450. Rohit’s Marks is equal to the twice the sum of Ram and Kirti’s marks. Amit marks are equal to Rohit’s marks.The person who gets 95 marks and above it will go to next level. Who are the people which go to next level examination?
A. Amit & Rohit
B. Rohit & Ram
C. Ram & Kirti
D. Kirti & Rohit
Let a, b, c, and d is the marks of Amit, Ram, Rohit and Kirti respectively.
Clearly, we have :
a+b+c+d=450….(i)
c=2(b+d) ….(ii)
a=c….(iii)
from i & ii
a+c+c/2 =450; (we have a=c)
c+c+c/2= 450
5/2c=450
c=180;
a=180
b+d= c/2= 180/2=90
a, c is more than 95, b, d is not more than 90.
Therefore, Amit and Rohit will go to next level examination.
6. State authority decided to make fence around the square garden of 400×400 m2. They decided to put poles at a distance of 10m. How many poles did they need altogether?
A. 100
B. 156
C. 108
D. None of these