Cummins Placement Paper
Cummins Aptitude Test
1. I bought a book for Rs 60, I sold off to a friend for Rs 70 but after a while I felt sorry, that I sold it and bought it back for Rs 80, how much loss did I incur?
A. Rs 10
B. Rs 15
C. Rs 20
D. Rs 50
Explanation:
cp of book=60
sp of book=70
profit=10
Again cp=80
Then loss =80-70=10.
2. Raj invested in Indigo, HUL and SBI shares at Rs. 300, Rs. 200 and Rs. 5 per share, 100 shares for Rs. 10000. The number of Indigo and HUL shares he bought are respectively:
A. 15, 25
B. 23, 17
C. 17, 23
D. 17, 60
Explanation:
Let the number of shares of indigo , HUL and SBI be x,y and z respectively.
Given, the total number of shares are 100 i.e.
=> x + y + z = 100 .............(i)
And total amount is 10000 i.e. the sum of the amounts of x shares of Indigo(300 Rs) , y shares of HUL(200 Rs) and z shares of SBI (5 Rs)
=> 300x+200y+5z=10000 ........(ii)
On solving the above two equations ,we finally get:
=>295x + 195y = 9500 (z term is to be cancelled by solving since we only need x(Indigo) and y(HUL)).
By substituting options in the final equation, we can check the answers .... i.e. x=17 and y= 23.
3. A rabbit is tied to one end of an equilateral triangle of side 5 m with a rope length of 8 m. The rabbit is not allowed to travel inside the triangle then find the maximum area covered by the rabbit?
A. (96/9) *pi
B. (480/9) *pi
C. (240/9) *pi
D. (100/9) *pi
Explanation:
The rabbit can graze up to 64*pi area if the triangle is not there.
But given that, it should not enter the triangle so it must avoid grazing the sector of the circle which covers the triangular area also. Each angle in the equilateral triangle is 60 degrees.
So the area of the sector formed by 60 degrees and of radius 8m is (pi*8*8*60)/360.
Therefore, maximum total area covered by the rabbit is given by:
=> Area of circle-area of sector
=> (pi*8*8) -(pi*8*8*60)/360
=> (480/9) *pi
4. In a covering a certain distance, the speeds of A and B are in the ratio of 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is?
A. 1 hour
B. 1 1/2 hour
C. 2 hours
D. 2 1/2 hour
Explanation:
Given, Ratio of speeds = 3:4
Then, Ratio of times taken = 4:3
Suppose A takes 4x hrs. and B takes 3x hrs. to reach the destination.
Then, 4x - 3x = 30/60 => x = 1/2
Time taken by A = 4x hrs. = 4 * 1/2 = 2 hrs.
5. A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
A. Rs. 375
B. Rs. 400
C. Rs. 600
D. Rs. 800
Explanation:
C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24
A's wages: B's wages: C's wages.
1/6: 1/8: 1/24 = 4:3:1.
C's share = 1/8 * 3200 = Rs. 400.
6. If average temperature of June, July and august is 31, and July, august, September is 30. Find temperature of September if temperature of June is 29?
A. 40
B. 36
C. 26
D. 30
Explanation:
Assume temperatures of June, July, August, September be a, b, c, d.
From the question,
=> (a+b+c)/3 = 31
=> a + b + c = 93. --------(1)
Also, (b+c+d)/3 = 30
=> b + c + d = 90. -------(2)
We also have temp of June to be 29 i.e a=29.
Therefore, substituting in first eqn.
We get, b+c =93-29 =64.
Now substituting b+c =64 in second eqn, we get
=> 64 + d = 90
=> d=26
Therefore, temperature of September is 26.
7. The L.C.M & H.C.F of two numbers is 84 & 21 respectively and the ratio of these two numbers is 1:4. Find the greatest number.
A. 75
B. 80
C. 84
D. None of these
Explanation:
We have a formula:
=>LCM * HCF = Product of 2 numbers
We are given that 2 numbers are in the ratio 1:4. So let the numbers be x and 4x. Substitute in the above formula to get the value of x.
=> 84 * 21 = x * 4x.
Solving the above equation, we get the value of x as 21.
So the two numbers are x and 4x.
Therefore, greatest number is 4x = 4 * 21 = 84.
8. Bhanu spends 30% of his income on petrol on scooter, 1/4 of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol, then what is the expenditure on house rent?
A. Rs.525
B. Rs.1000
C. Rs.675
D. Rs.175
Explanation:
Let Bhanu's income be Rs x.
Then, according to the question,
30% of x = 300
=> x = 300 * 100/30 = Rs 1000.
Balance = 1000 - 300 = 700.
Hence, Rent = 1/4 of 700 = Rs 175.
9. A mixture of 50 liters of milk and water contain 10% of water. How much water must be added to make water 20% in the given mixture?
A. 7 liters
B. 10 liters
C. 6 liters
D. 5 liters
Explanation:
According to question,
Quantity of Water = 10% of 50 = 5 liter.
and, Milk = 45 liter
Let x br the amount of water to be added.
Now,
=> (5 + x) = 20% of (45 + x).
=> 5 + x = (45 + x) / 5.
=> 25 + 5x = 45 + x
=> 4x = 20
=> x = 5 liter.
10. An express A starts at 2.30 pm from nampali station and travels towards vizag station at speed of 80 kmph. Another express starts at 4.30 pm from nampali station to vizag station at speed of 100 kmph. How far away from station Nampali will the two trains meet??
A. 600 km
B. 700 km
C. 750 km
D. 800 km
Explanation:
Let train A take x hours to reach the point of meeting (let it be P)
Then train B will reach the same point in x-2 hours.
Distance covered to reach P by train A in x hours=Distance covered by B to reach P in x-2 hrs.
=> 80*x = 100(x-2)
=> 80x = 100x-200
=> x = 10 hrs.
Distance from Nampali = x*speed of train A.
=> 10*80 = 800 km.
Cummins Logical Reasoning Test
11. Syllogism:
Statements: No holiday is a vacation.
Some vacations are trips.
Conclusions:
(I) No trip is a holiday.
(II) Some holidays are definitely not trips.
A. if only conclusion I follows.
B. if only conclusion II follows.
C. if either conclusion I or II follows.
D. if neither conclusion I nor II follows.
E. if both conclusions I and II follows.
Answer: D.
12. Syllogism:
Statements:
All towns are cities
All cities are urban
Some urban are rural
Conclusions:
(I) Some towns are rural
(II) All rural are towns
A. if only conclusion I follows.
B. if only conclusion II follows.
C. if either conclusion I or II follows.
D. if neither conclusion I nor II follows.
E. if both conclusions I and II follows.
Answer: D.
13. Blood Relation:
If A is B's brother, B is C's sister and C is D's father, D is A's...
A. Brother
B. Sister
C. Nephew
D. Cannot be determined
E. None of these
Explanation:
A is the brother of B. (A is male) B is sister of C. (B is female) C is father of D.
(C is male) The sex of D is not known. A and C are brothers of B. A is the uncle of D.
Since, sex of D is not clear, we cannot determine what is D to A.
14. Blood Relation:
A man pointing to a photograph says, "The lady in the photograph is my nephew's maternal grandmother. How is he lady in the photograph related to the man's sister who has no other sister?
A. Cousin
B. Sister
C. Mother
D. Mother-in-Law
Explanation:
The only is the grandmother of man's sister son. i.e. The mother of the mother of man's sister's son i.e. The mother of man's sister.
15. Directions & Distances: -
The town of Paranda is located on Green Lake. The town of Akram is west of Paranda. Tokhada is east of Akram but west of Paranda. Kakran is east of Bopri but west of Tokhada and Akram. If they are all in the same district, which town is the farthest west?
A. Paranda
B. Kakran
C. Akram
D. Bopri
Answer: D.
16. Ordering & Ranking: -
In a queue of children, Arun is fifth from the left and Suresh is sixth from the right. When they interchange their places among themselves, Arun becomes thirteenth from the left. Then, what will be Suresh's position from the right?
A. 8th
B. 14th
C. 15th
D. 16th
Explanation:
Since Arun and Suresh interchange places, so Arun's new position (13th from left) is the same as Suresh's earlier position (6th from right).
So, number of children in the queue = (12 + 1 + 5) = 18.
Now. Suresh's new position is the same as Arun's earlier position fifth from left.
Therefore, Suresh's position from the right = (18 - 4) = 14th.
17. Ordering & Ranking: -
Among P, Q, T, A and B each having a different height, T is taller than P and B but shorter than A and Q. P is not the shortest. Who among them is the tallest?
A. A
B. Q
C. P
D. P or B
E. Data inadequate
Explanation:
T > P, B
T < A, Q
P > B
A, Q > T > P > B
So, either A or Q is the tallest
18. Choose odd letter group:
PRVX, MQTV, DHKM, BFIK
A. PRVX
B. MQTV
C. DHKM
D. BFIK
Explanation:
In all other groups, the first, second and third letters are respectively moved four, three and two steps forward to obtain second, third and fourth letters respectively.
19. Coding-Decoding:
If ROSE is coded as 6821, CHAIR is coded as 73456 and PREACH is coded as 961473, what will be the code for SEARCH?
A. 246173
B. 214673
C. 214763
D. 216473
Explanation:
The letters are coded accordingly S as 2, E as 1, A as 4, R as 6, C as 7 and H as 3. i.e., 214673.
20. Data Sufficiency:
Five friends P, Q, R, S and T are standing in a row facing East. Who is standing at the extreme right end?
(I) Only P is between S and T; R is to the immediate right of T.
(II) R is between T and Q.
A. statement I alone are sufficient to answer the question, statement II alone not sufficient to answer the question;
B. statement II alone are sufficient to answer the question, statement I all are not sufficient to answer the question;
C. Either statement I alone or statement II alone are sufficient to answer the question;
D. Even in both statements I and II together are not sufficient to answer the question;
E. Both statements I and II together are necessary to answer the question.
Explanation:
From I: SPTR
From II: I R Q
Combining I & II, we get, S P T R Q.
Hence Q is at extreme right.
Cummins Verbal Ability Test
21. Fill in the blank:
He travelled all ___________ the world when he was eighty years old.
A. in
B. over
C. with
D. of
Answer: B.
22. Fill in the blank:
He drove from Maharashtra ____________ Karnataka without stopping to rest.
A. Is
B. to
C. into
D. towards
Answer: B.
23. Synonym:
supervene
A. intervene
B. overreach
C. displace
D. follow
Answer: D.
24. Antonym:
able
A. willful
B. inept
C. careful
D. feasible
Answer: B.
25. One Word Substitution:
One who is unable to read or write:
A. Genius
B. Illiterate
C. Palisade
D. Pulverize
Answer: B.
26. Direct & Indirect Speech:
Rajesh said, "I bought a car yesterday."
A. Rajesh said that I have bought a car the previous day.
B. Rajesh told that he had bought a car yesterday.
C. Rajesh said that he bought a car the previous day.
D. Rajesh said that he had bought a car the previous day.
Answer: D.
27. Active & Passive Voice:
People claim to have seen the suspect in several cities.
A. The suspect is being seen in several cities
B. The suspect has been the people in several cities
C. The suspect is claimed to have been seen in several cities
D. The suspect was seen by people in several cities
Answer: C.
28. Sentence Arrangement:
A. He felt justified in bypassing Congress altogether on a variety of moves.
B. At time, he was fighting with the entire Congress.
C. Bush felt that he had a mission to restore power to the presidency.
D. Bush was not fighting just with the democrats.
E. Representative democracy is a messy business, and a CEO of the White House does not like a legislature of second guessers and time wasters.
F. CAEDB
G. DBAEC
H. CEADB
I. ECDBA
Answer: D.
29. Error Spotting:
No sooner we entered a./ than he got up b./ and left the room. c./ No error. d.
A. a
B. b
C. c
D. d
Explanation:
Insert 'had' after 'sooner'
30. Error Spotting:
The teacher drew (a)/ and attention of the boys (b)/ to the importance of regular practice. (c)/ No error (d)
A. a
B. b
C. c
D. d
Explanation:
Say 'the attention'
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