SSC CHSL Arithmetic Aptitude  Question Paper free Sample Model Question Paper with answer and solution

1.    3/5th of a number is more than 40% of the same number by 35. What is 80% of that number ?
a)    175
b)    105
c)    150
d)    140    (Ans)

2.    The sum of two digits of a number is less than the number by 54. What is the difference between two digits of the number ?
a)    2
b)    4
c)    6
d)    Data inadequate   (Ans)

3.     In the equation given below which number (approx.) will replace the question mark ?   6.59 x 149.36 + 159% of 1642 = 10000 - ?
a)     6800 
b)    7500
c)    6500 (Ans)
d)    5500

4.    The inequality of b² + 8b > 9b + 14 can be removed if -----
a)    b> 5, b< -5
b)    b> 5, b< - 4     (Ans)
c)    b > 6, b< -6
d)    b > 4, b < -4

Explanation : b² + 8b - 9b -  14 > 0
                          b² -b -  14 > 0
                          b² - b  + 1/4 > 14  +1/4
                          (b-1/2) >  +  √57/2
                          b>    1 +   7.55
                                         2       
                          > 4.28 or - 3.28
       :.                 b  > 5 or b < - 4

5.    If the radius of the base and the height of a right circular cone are increased by 20%, then what is the approximate percentage increase in volume ?
a)    60
b)    68
c)    73     (Ans)
d)    75

Explanation : 2a + b +    a² +2ab +      a²b     (Here a = 20=b)
                                           100        10000                  
      = 2 x 20 + 20+   (20)² + 2 x 20 x 20    +         (20)² x 20
                                                100                        10000
      = 40 + 20 +    1200 +   8000
                            100      10000
       = 72.8 = 73 (Approx.)
6.
 
PQRS is a diameter of a circle of radius 6 cm as shown in the figure above. The lengths PQ, QR and RS are equal. Semi-circles are drawn on PQ and QS as diameters. What is the perimeter of the shaded region ?
a)    12 Π     (Ans)
b)    14 Π
c)    16 Π
d)    18 Π 

7.    In the equation given below, what (approx.) number will replace the question mark ?
       162 √7+18068 - 2 and 1/7 of 5162 = ?
a)    7200
b)    8700
c)    9200
d)    7600  (Ans)

8.    In the equation given below what will come in place of question mark ?  5672 + 3805 = ? + 39846
a)    21615
b)    20031
c)    219751
d)    20751  (Ans)

9.    When 40% of a certain number is added in an other number, then the second number is increased by its 60%. What is the ratio between the two numbers ?
a)    3:2 (Ans)
b)    2:3
c)    3:4
d)    Data inadequate 

10.  The average marks of 55 students of a class is 60. The average marks of passed students is 70 and the average marks of failed students is 45. What is the number of failed students ?
a)    33
b)    22 (Ans)
c)    28
d)    Data inadequate

Directions (Q.11-15) Each of the question below consists of a question and three statements numbered I, II and III. You have to decide which of the statements are sufficient to answer the question.
11.    What will be difference between the ages of P and Q after 6 years ?
(i)      The ratio between the present ages of P and Q is 3:5
(ii)     The ratio between the present age of P and his age after 6 years is 3:4
(iii)    The ratio between the present age of Q and his age after 6 years is 5:6
a)     Any two of the above statements together are necessary      (Ans)
b)    All the three statements together are necessary
c)    Only (i) and (ii) together are necessary
d)    Only (i) and (iii) together are necessary

Explanation :    The equations from the three given statements are :
                           P       =    3
                           Q             5                   ----(i)
                      P            =    3
                  P + 6                4                  ----(ii) 
and               Q            =    5
                  Q+ 67              6                  ----(iii)
     :. From any two equations the value of P and Q can be determined and then their difference can be calculated .

12.  What is the speed of moving train ?
(i)    This train crosses another train coming from opposite direction in 72 seconds
(ii)    The length of the first train is 100 metres
(iii)    The length of the second train is 180 metres
a)     All the three statements together are necessary   
b)     All the three statements together are not sufficient    (Ans)
c)     Only (ii) and (iii) together are necessary
d)     Only (i) and (ii) together are necessary

Explanation :    As the speed of first train is not given, so the speed of second train cannot be found

13.   What was Q's share in the money ?
a)     P received Rs.1200 more than R
b)    Q received Rs.800 more than P
c)     R received Rs.1600
a)    Only statements (i) and (ii) together are necessary
b)    Statements (i) and (ii) or (iii) are necessary
c)    All the three statements together are necessary  (Ans)
d)    All the three statements together are not sufficient 

Explanation :    The equations from the given statements are :     R = 1600
                                                                                                            P-R  = 1200
                                                                                and                     Q-P  = 800
                            :. In order to find the value of Q, all the equations are necessary.

14.  What sum of money did Prakash borrow from Arun ?
(i)    Arun received Rs.6400 from Prakash after 8 years as S.I.
(ii)    Prakash invested 50% of the borrowed money and received Rs.8000 in return of this investment
(iii)   Total S.I. after 4 years was 20% of the total sum of money 
a)    Only statements (i) and (ii) together are necessary
b)    Only statements (i) and (iii) together are necessary  (Ans)
c)    All the three statements together are necessary
d)    All the three statements together are not sufficient 

Explanation :    From statement (i)     6400 = X x 8 x r
                                                                       100
                              Hence, the value x can be obtained from statements (i) and (iii) 
                                           

15.   What profit per cent did Arun earn by selling his car ?
(i)    Instead of purchasing a motor cycle Arun purchased a car and paid Rs.60000
(ii)    Arun has purchased his motor cycle for Rs.25000
(iii)   Arun sold his car for Rs.1,10,000
a)    Only (i) and (ii) are necessary
b)    Only (ii) and (iii) are necessary
c)    All the three statements together are necessary  (Ans)
d)    All the three statements together are not sufficient