NUMERICAL ABILITY--24-12-2012
1.                   The difference between the local value and base value of 7 in the numeral 657903 is:
a. 0                 b. 7896            c. 6993                        d. 903
2.                   The sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the numbers is:    a. 7                 b. 29                c. 41                d. 67
1. The unit’s digit in the product (3127)173  is:  a. 1                 b. 3                  c. 7                  d. 9
1.  (51+52+53+………+100) is equal to:   a. 2525           b. 2975            c. 3225                        d. 3775
1. 5b2 is a three-digit number with b as a missing digit. If the number is divisible by 6, the missing digit is:   a. 2                 b. 3                  c. 6                  d. 7
6.       A mixture of 85 kg contains milk and water in the ratio 27 : 7. How much more water is to be added to get a new mixture containing milk and water in the ratio 3:1?
a) 5 kg     b)6.5 kg           c) 7.5 kg          d) 8 kg
7.       The ages of Raju and Biju  are in the ratio 3:1. Fifteen years hence, the ratio will be 2:1. Their present  ages are:             a) 30yrs, 10yrs             b) 45 yrs, 15yrs  c)21 yrs, 7 yrs          d) 60yrs, 20yrs
8.       The speeds of three motor bikes are in the ratio 6 : 5 : 4.  The ratio between the time taken by them to travel the same distance is : a) 10 : 12 : 15     b) 12 : 10 : 8    c) 15 : 12: 10   d) 10 : 15 : 12
9.       In a company 10% of male staff are same in number as 1/4th of the female staff. What is the ratio of male staff to female staff             a) 3 : 2             b) 5 : 2                        c) 2 : 1             d) 4 : 3
10.    The telephone bill of a certain establishment is party fixed and partly varies as the number of calls consumed. When in a certain month 540 calls made the bill is Rs.1800. In another month 620 calls are consumed then the bill becomes Rs.2040. In another month 500 units are consumed due to more holidays. The bill for that month would be : a) Rs.1560           b) Rs.1680      c) 1840            d) Rs.1950
11) The  average  mark  of  a  class  of  twenty  students  is  64.  If  three  students  whose  marks  are  32,28  and  34  are  removed  ,  then  find  the  approximate  average  mark  of  the  remaining  students  of  the  class.       a. 71      b. 74       c. 57       d. 70
12) The  number  of  students  in  the  three  sections  of  a  class  are  in  the  ratio  2:3:4.  The  average  marks  scored  in  each  of  these  sections  is  in  the  ratio  4:3:1.  By  what  percent  is the  average  mark  of  the  second  section  more  than  the  class  average?
a. 23.27%                    b. 28.57%              c. 32.38%              d. 36.74%
13) The  average  age  of  40  students  is  8 years.  If  the age of  teacher  is  also  included  , then  their  average  age  increases  by half  a  year.  What  is the age  of  the  teacher?
a.  45 years                 b. 48.5 years         c. 28.5 years      d. 26.5 years
14) Eight  kilograms of  rice  costing Rs. 16  per  kg  is  mixed  with four  kilograms of rice  costing  rs.22 per  kg.  What  is  the  average  price  of  the  mixture?     a. 20   b. 18          c. 16         d. 19
15) How  many  kilograms  of  tea  powder costing   Rs. 31  per  kg  be  mixed  with  36  kilograms  of  tea  powder  costing  Rs. 43 per kg,  such  that  the  mixture  when  sold  at  Rs. 44 per kg  gives  profit  of 10%?        a. 12                b. 15       c. 20       d. 10

1.C          2.D          3.C          4.D          5.A          6.A          7.B          8.A          9.B          10.B

11.D       12.B       13.C       14.B       15.A

1. Ans: c.
(Local value)-(Face value)= (7000-7)=6993.
1. Ans: d
x+(x+36)+y=100 => 2x+y=64
Therefore y must be even prime, which is 2.
Therefore 2x+2=64 => x=31
Third prime number= (x+36)= (31+36)= 67.
1. Ans: c
Unit digit in (3127)173  =  Unit digit in 7173. Now, 74 gives unit digit 1.
Therefore, 7173= (74)43 * 71. Thus, 7173 gives unit digit 7.
1. Ans: d
(51+52+53+………+100) = (1+2+3+…….+100)- (1+2+3+4+……+50)
= (100*101)/2  -  (50*51)/2
= (5050-1275)= 3775.
1. Ans: a
Let the number be 5b2. Clearly, it is divisible by 2.
Now, 5+b+2= (7+b) must be divisible by 3. So, b= 2.
6. Expl : Milk in 85 kg of mix = 85* (27/34) = 135/2 kg.
Water in it = 85-135/2 = 35/2 kg.
Let x kg of water be added to it.
Then, (135/2)/(35/2 + x) = 3/1;  135/(35 +2x) = 3/1;
105 + 6x = 135 ; 6x = 30; x = 5
The quantity of water to be added = 5 kg
7. Expl : Let the ages of raju and Biju is 3x and x years respectively.
Then, (3x +15)/ (x+15) = 2/1;   ->   2x + 30 = 3x + 15 -> x = 15
So Raju’s age = 3*15 = 45 and Biju’s age  = 15 years
8. Expl :  Ratio of time taken : 1/6 :1/5 : 1/4  = 10 : 12 : 15
9. Expl : 10% of MS = 1/4th of FS -> 10MS/100 = 1/4FS  -> MS = 5/2 FS
:. MS/FS = 5/2 = MS : FS = 5 : 2
10. Expl : Let the fixed amount be Rs. X and the cost of each unit be Rs. Y.
Then, 540y + x = 1800 …. And 620y + x =  2040
On subtracting (i) from (ii), we get 80y = 240 -> y = 3
Putting y = 3 in (i) we get :
540 * 3 +  x = 1800 x = (1800-1620) = 180
. :  Fixed charges = Rs.180, Charge per unit = Rs.3.
Total charges for consuming 500 units = 180 +(500*3) = Rs.1680
11. Exp. Total  mark  of  20 students  =  64*20  =  1280,
Total  mark  after  the  removal  of  3 students  =  1280 –(32 +28+34 )
=   1280 – 94  =  1186
Approximate average  mark = 1186/(20-3)  =  1186/ 17 =  70
12. Exp.  Let  the  number  of  students  be  2x, 3x, 4x.
Let  the  average  marks  be  4y,3y,y.
Average  mark of class = ( 8xy+9xy+4xy)/(2x+3x+4x) =21xy/9x=7y/3
Percentage  difference  = ( 3y -  7y/3)/7y/3 *100 =  28.57%
13. Exp.  Total  age  of  40  students  =  40*8 = 320
Let  the age of  the the  teacher  be x,  Then (320+x)/41 = 8+1/2 =8 ½.
320+x =17/2*41  =697/2 = 348.5,  x  =348.5-320  = 28.5
14. Exp.  P1 = Rs.16 per kg,  p2  = Rs. 22 per kg,  q1 = 8 kg,  q2  =  4 kg
Now ,  p  =  (p1q1+p2q2)/(q1+q2)
Average  price  of  the  mixture  =  8*16+4*22/12  = 128+88/12
=  216 /12  =  18
15. Exp. SP  of  the  mixture  =  44,  Profit  =10%,  Then  CP  =  SP*100/110
44*100/110 =  Rs. 40 per kg
Using  alligation  rule,  the  required  ratio =

= 1:3
If    36 kg  is  3  part  then  1  part  is   36*1/3   =12