SOLUTION TO CUMMINS PLACEMENT PAPER. GENERAL APTITUDE QUESTION: 1.  A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:  Answer: Option B Explanation: Let the required number of revolutions made by larger wheel be x. Then, More cogs, Less revolutions (Indirect Proportion) 14 : 6 :: 21 : x 14 x x = 6 x 21 x = 9. 
Direction (for Q.No. 2): Insert the missing number.  2.  8, 24, 12, 36, 18, 54, (….)  Answer: Option A Explanation: Numbers are alternatively multiplied by 3 and divided by 2. So, the next number = 54 ÷ 2 = 27. 
3.  A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:  Answer: Option B Explanation: Speed of the train relative to man =   125  m/sec  10 
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x – 5) km/hr. x – 5 = 45 x = 50 km/hr. 
Direction (for Q.No. 4):  4.  A man mixes two types of rice (X and Y) and sells the mixture at the rate of Rs. 17 per kg. Find his profit percentage.  I.  The rate of X is Rs. 20 per kg.  II.  The rate of Y is Rs. 13 per kg. 
  A.  I alone sufficient while II alone not sufficient to answer 
  B.  II alone sufficient while I alone not sufficient to answer 
  C.  Either I or II alone sufficient to answer 
  D.  Both I and II are not sufficient to answer 
  E.  Both I and II are necessary to answer 

Answer: Option D Explanation: The ratio, in which X and Y are mixed, is not given. So, both I and II together cannot give the answer. Correct answer is (D). 
5.  In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:  Answer: Option A Explanation: Number of valid votes = 80% of 7500 = 6000. Valid votes polled by other candidate = 45% of 6000 
6.  A father said to his son, “I was as old as you are at the present at the time of your birth”. If the father’s age is 38 years now, the son’s age five years back was:  Answer: Option A Explanation: Let the son’s present age be x years. Then, (38 – x) = x 2x = 38. x = 19. Son’s age 5 years back (19 – 5) = 14 years. 
7.  A person’s present age is twofifth of the age of his mother. After 8 years, he will be onehalf of the age of his mother. How old is the mother at present?  Answer: Option C Explanation: Let the mother’s present age be x years. Then, the person’s present age =   2  x   years.  5 
2(2x + 40) = 5(x + 8) x = 40. 
8.  A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:  Answer: Option C Explanation: 2(15 + 12) x h = 2(15 x 12) Volume =   15 x 12 x  20  m^{3}  = 1200 m^{3}.  3 

Direction (for Q.Nos. 9 – 10): Find out the wrong number in the series.  9.  3, 7, 15, 39, 63, 127, 255, 511  Answer: Option C Explanation: Go on multiplying 2 and adding 1 to get the next number. So, 39 is wrong. 
10.  190, 166, 145, 128, 112, 100, 91  Answer: Option D Explanation: Go on subtracting 24, 21, 18, 15, 12, 9 from the numbers to get the next number. 190  24 = 166 166  21 = 145 145  18 = 127 [Here, 128 is placed instead of 127] 127  15 = 112 112  12 = 100 ... and so on. Therefore, 128 is wrong. 
11.  The true discount on a bill of Rs. 540 is Rs. 90. The banker’s discount is:  Answer: Option B Explanation: P.W. = Rs. (540 – 90) = Rs. 450. S.I. on Rs. 450 = Rs. 90. S.I. on Rs. 540 = Rs.   90  x 540   = Rs. 108.  450 
B.D. = Rs. 108. 
13.  A sum of Rs. 1360 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B’s share is:  Answer: Option C 
Direction (for Q.No. 16):  16.  What is the rate of interest p.c.p.a.?  I.  An amount doubles itself in 5 years on simple interest.  II.  Difference between the compound interest and the simple interest earned on a certain amount in 2 years is Rs. 400.  III.  Simple interest earned per annum is Rs. 2000. 
  A.    B.    C.    D.    E.  I only or II and III only 

Answer: Option E Explanation: I.  P x R x 5  = P R = 20.  100 
II. P   1 +  R   2  – P –  P x R x 2  = 400 PR^{2} = 4000000.  100  100 
III.  P x R x 1  = 2000 PR = 200000.  100 
 PR^{2}  =  4000000  R = 20.  PR  200000 
Thus I only or (II and III) give answer. Correct answer is (E). 
17.  If 40% of a number is equal to twothird of another number, what is the ratio of first number to the second number?  Answer: Option C Explanation: A : B = 5 : 3. 
18.  Three numbers which are coprime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is:  Answer: Option C 
20.  A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?  Answer: Option B Explanation: Area of the park = (60 x 40) m^{2} = 2400 m^{2}. Area of the lawn = 2109 m^{2}. Area of the crossroads = (2400 – 2109) m^{2} = 291 m^{2}. Let the width of the road be x metres. Then, 60x + 40x – x^{2} = 291 x^{2} – 100x + 291 = 0 (x – 97)(x – 3) = 0 x = 3. 
 
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