# WBCS- 2011 (Compulsory) Arithmetic & Test Of Reasoning

WEST BENGAL CIVIL SERVICE

EXAMINATION, 2008

COMPULSORY PAPER ARITHMETIC AND TEST OF REASONING

Time Allowed: 3 hours                                                                                   Full Marks: 100

Group - A (50 Marks ) (Arithmetic)

1. Simplify:

$$\frac{{\frac{3}{7} - \frac{2}{9}}}{{\frac{3}{7} + \frac{2}{9}}}of2\frac{{11}}{{26}} \div \frac{4}{{13 - 3\frac{8}{9}}} - \frac{{88}}{{1 + \frac{1}{{6 - \frac{3}{{13}}}}}}$$

2.  (a)  Find two consecutive positive even integers whose product is 440.

(b)  Divide Rs. 195 among Ram, Rahim, Ronn so that  $${1 \over 2}$$ of Ram's share, $${3 \over 2}$$ of Rahim's share and $${3 \over 5}$$ of Ronn's share may be equal.             2+3

3.  A bag contains Rs. 325 in the form of 1 rupee, 25 paise and 50 paise coins in the ratio 3 : 4 : 5  .Find the number of each type of coins.         5

4.  (a) In an Examination 17% of the candidates fail in Bengali and 18% in English. If 5% fail in both Bengali and English, find the percentage of those who pass in both the subjects.

(b) An article was sold at a loss of 3%. Had it been sold for Rs. 16 more, there would have been a profit of 5%.  Find the cost price.         2+3

5.  Gahana lent Rs. 5,000 to Sabina for 5 years and Rs. 6,000 to Sophie for 3 years. Find the rate of interest if Gahana gets an interest of Rs. 860 at the end.       5

or,

Before 5 years, ratio of ages A and B was 10 : 14.  After 5 years, the ratio would be 12 : 16 .   Find their present ages.       5

6.  An A.C. machine is priced at Rs.12,000 and is sold at a discount of 10%. There is a further off-season discount of 5% on the net amount.  How much does the customer pay for the A.C. machine ?      5

7.  In an election for a Corporation seat, there were two candidates.  A total of 9735 votes were polled. 105 votes were declared invalid. The successful candidate got 5 votes his opponent had. By what margin did the successful candidate win ?       5

8.  (a)  Due to some error in the weighing machine, Rahul's weight was shown as 72 kg. as against the actual value of 80 kg.  Find the percentage of error.

(b)  The sum of two numbers is 256.  If 32 is their H.C.F, find the numbers.       3+2

9.  The total price of a cow and a horse is Rs. 4,000.  If the price of the cow is increased by 25% and that of the horse is increassed by 20%, then their total price becomes Rs.4,900. Find the price of the cow.     5

10.  A motor boat moving at 8 km/hr. in still water goes 12 km. down stream and comes back in total of 4 hours. Determine the speed of the water.     5

Group B (50 marks) (Test of Reasoning)

11. (a) What is the value of $$105 \time 95 ? (i) 9900 (ii) 9975 (iii) 10025 (iv) 9925 (b) What is the value of [tex]7.61 \times 7.61 + 2 \times 7.61 \times 2.39 + 2.39 \times 2.39$$  ?

(i) 100      (ii) 77.61      (iii) 23.39       (iv) 22.39           2+3

12.  (a) Provide the number in the place of asterisk:

3 + 5 + 7 + ...........   + up to 98 terms = *

(b) $$^n{P_1} = n(n - 1)(n - 2) \cdots \cdots (n - r + 1)$$  find n, where  $$^n{P_4} = 360$$        2+3

13.  (a)  From the following set of words, select that one which does not conform to the others :

kitten,    calf,    foal,   wolf

(b)   From the collection of 4 numbers, select that one which does not conform to the other:

121,   144,    289,    293

(c)   Write down the sensible word that can be formed by rearranging the letter

(i)  DEMNOR,        (ii) CTAMAESHMIT          1+2+2

14.  (a)  If A : B = 2 : 3,     B : C = 4 : 5,      C : D = 6 : 7,    find  A : D

(b)  If  x : y = 3 : 4 ,     find (7x + 3y) : (7x - 3y)

(c)  If  $$f\left( x \right) = {3^x} + {1 \over {{3^x}}} + 1$$ ,  find the value of  $$f\left( { - x} \right)$$       1 +2+2

15.  (a) if (a, b) * (c, d) = (a + d) - c/d , find (1, 2) * (3, 4)

(b) If f is a function defined by $$f\left( x \right) = {x \over c}$$  where $$c \ne 0$$ , find $$\left( {{1 \over c}} \right)f$$        2+3

16.  (a) Which number will occupy the blank space ?

(b) If the average of  a  and  b  is 15,  the average of  b and c  is  12  and the average of  a  and  c  is 13,  find the value of b .       2+3

17.  (a) In a certain code language

'1 2 3' means 'hot filtered coffee'

'3 5 6' means 'very hot day'

'5 8 9' means 'day and night'

which of the following numeral stands for  'very' ?

(i) 9,       (ii) 2,      (iii) 3,       (iv) 6

(b) Girija,  Ishan,  Francis and Zaved are sitting on a bench.  Francis has Zaved next to him on his left. Ishan is sitting with Francis and Girija on either of him.  Who sits at the extreme right ?          3+2

18.   (a) In the following four numbers, three are same in a certain way while the rest one is different. Find out the different one.

(i) 14,     (ii) 35,      (iii) 63,     (iv) 72

(b)  Choose the correct one if the sequence given below were continued.

3+2

19.  (a) If B's mother was As mother's daughter, how was A related to B ?

(i) father,    (ii) paternal uncle,     (iii) maternal uncle,      (iv) brother

(b)  $${2^{71}} + {2^{72}} + {2^{73}} + {2^{74}} + {2^{75}}$$ is divisible by

(i) 11,     (ii) 13,      (iii) 31,     (iv) 7

(c)   In the following, three pairs are related in some way and one pair is differently related. Find out the different one:

(i) Crime-punishment,    (ii) Judgement-advocacy,     (iii) Enterprise-success,     (iv) Exercise-health        1+2+2

20.  (a) Statement: Soldiers serve their country.  There are three inferences.  Choose the correct one:

(i)   Those who serve their country are soldiers,

(ii)   Men generally serve their country,

(iii)  Some men who are soldiers serve their country.

(b)  Statement:

(i)  Gunen is an artist,  (ii)  Artists are beautiful. Which of the following conclusion is correct logically ?

(i)  Gunen is beautiful,

(ii)  All beautiful persons are artist,

(iii)  All artists are beautiful

(c)  Below is given a statement followed by two assumptions. Decide which of the assumption is implicit in the statement:

Statement: The pen is mighter than sword.

Assumption : (i) The pen is made of strong metal than the sword    (ii)  The power of the mind is much stronger than brute physical powe.

(i)  Onli one I is implicit

(ii)  Onli one II is implicit

(iii)  both I and II are implicit

(d)  Which one is different from the rest of the others ?

(i) Japan     (ii) China      (iii) france     (iv)  Nepal.

(e)   In the following these are alike in certain way. Which is the one not like the other three ?

(i) Algebra      (ii)  Mathematics      (iii) Arithmatic     (iv)  Geometry.        5

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