# CTS Aptitude Question paper

CTS Apti Question paper

1. If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by Ans: 330

2. The total no. of numbers that are divisible by 2 or 3 between 100 and 200(both inclusive) are Ans:67

3. From a pack of cards Jack, Queen, King & ace are removed. Then the algebraic sum of rest of the cards is Ans:216

4. The average temperature of days from Monday to Wednesday is 37 degree Celsius and that of from Tuesday to Thursday is 34 degrees. The temperature of Thursday is 4/5th of Monday. Then the temperature of Thursday is

Ans: 36 degrees

5. Swetha, Tina, Uma and Vidya are playing a gambling. In this different people lose in different games-in the reverse alphabetical order. The rule is that if one loses she should double the amount of others. At the end of 4th game each of them have same amount of money (Rs.32). Which one of them started with the least amount? (6) Which one of them started with the largest amount of money? (7.) At the end of the 2nd game what is the amount of money with uma?

Ans: Vidya, Swetha, Rs.8

8. A cube of 12 mm is painted on all its side. If it is made up of small cubes of size 3mm. If the big cube is splitted into those small cubes, the number of cubes that remain unpainted is Ans: 8

9. B is 50% faster than A. If A starts at 9 A.M. and B starts at 10 A.M. A travels at a speed of 50 km/hr. If A and B are 300 kms apart, The time when they meet when they travel in opposite direction is Ans:12 noon

10. A graph will be there. Inside the graph sheet there will be a Quadrilateral. We have to count the number of squares in the Quadrilateral.

11. You are having 31kg of rice. You are provided with a 1kg stone for weighing. In how many weights the 31kg of rice can be weighed. Ans: 5

12. A starts at 11:00AM and travels at a speed of 4km/hr. B starts at 1:00PM and travels at 1km/hr for the first 1hr and 2km/hr for the next hr and so on. At what time they will meet each other. Ans:

13. There are 80 coins, among them one coin weighs less compared to other. You are given a physical balance to weigh. In how many wieghings the odd coin can be found. Ans:

14. Dia of the circle 4cm. The shaded part is 1/3 of the square area. What is the side of the square. Ans: root of 3pi

15. A,B,C, can do a work in 8,14,16 days respectively. A does the work for 2 days. B continues from it and finishes till 25% of the remaining work. C finishes the remaining work. How many days would have taken to complete the work Ans:

16. Raja went to a beauty contest .his wife was eager to know the result he told that the lady wear a yellow sari was winner. Miss. Andhra Pradesh Miss. Utter Pradesh, Miss. Maharashtra, Miss. West Bengal were the participants all the participants sat in a row. The conditions are (A) The woman wore yellow sari won the competition. (B) Miss. West Bengal was neither the runner-up or winner.(C) Miss. West Bengal was not at either ends.(D) Miss. Maharastra wore the white sari.(E) The women wore white sari and yellow sari sat at extreme ends.(F) The runner-up and winner did not sit together. [This was the passage given and the questions were easy]

17. The ratio of white balls and black balls is 1:2. If 9 gray balls is added it becomes 2:4:3. Then what is number of black balls. Ans:12

18. There are 10 coins. 6 coins showing head. And 4 showing tail. Each coin was randomly flipped (not tossed) seven times successively.after flipping the coins are 5 heads 4 tails one is hided the hided coin will have what.

19. Two cars are 500 cm apart. each is moving forward for 100 cm at a velocity of 50 cm/s and receding back for 50 cm at 25 cm/s at what time they will collide with each other.

20. People near the sea shore are leading a healthy life as they eat fish.but people at other part of the city are also healthy. Inference.

21. It is found from research that if u r a drunken then u have a less chance for chronic heart diseases. Inference.

22. A-B+c>A+B-C i) B is +ve, ii) B is �ve when it will hold true.

23. i) C.P is Rs 120 and profit is 30%

ii) C.P is Rs 210 and profit is 20%

we can find the S.P by using

i)only ii)only both i &ii neither i&ii

24. How will u find distance between Nagpur and Mumbai?

I took one hour more when I travel at 80 km/hr than at 90 km/hr.

25. 100 coins were collected by four persons each collected more than 10 each collected a different number each was an even number find what is the max possible no of coins, two more questions based on the same passage.

26. A car travels from B at a speed of 20 km/hr. The bus travel starts from A at a time of 6 A.M. There is a bus for every half an hour interval. The car starts at 12 noon. Each bus travels at a speed of 25 km/hr. Distance between A and B is 100 km. During its journey , The number of buses that the car encounter is

27. The ratio of the ages of the father and the son is 5:3, After 10 years it will be in the ratio 3:2. What will be their ages.

28. There was a Island. In that Island there was Rubys and Emeralds. Those were available in plenty. 0.3 kg of ruby is 4 lakhs and 0.4 kg of emeralds is 5 lakhs. Jayanth is buying 12 kg of Ruby and emerald. Choices will be given . Jayanth has to carry both ruby and emerald to the maximum profit.

29. Varun buys 8 books,10 pens and 2 pencils and Babu buys 6 books, 5pens and 5 pencils. Babu pays 50% more than Varun. What is the amount Varun spends in buying pencils.

30. Prakash and Revathi rent a fancy shop. Prakash imposes the following restrictions on Revathi for buying clips,stickers and lip sticks. The number of clips is twice the no. of stickers. The no. of lipsticks should be more than the sum of clips and stickers. Cost of clip is 1 rupee. Cost of lipstick is twice the clips. Cost of 1 lipstick is the cost of four stickers. Then What is the amount that Prakash spents for Revathi. Answer choices will be given.

#### kumar_sarma2000 Profile Answers by kumar_sarma2000 Questions by kumar_sarma2000

• May 13th, 2007

If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by

the solution is as follows:
1)sum of numbers from 1 to 100 is 5050

2)numbers having 6 are 6,16,..56,60,61,...69,76,86,96 whose sum is 1089.

3)remove the above sum from 5050 we get 3961.

4)replace 6 in numbers in step 2 with 9,which we get 9,19,..59,90,91,..99,79,89,99 whose sum is 1419.

5)add above sum to 3961 we get 5380.

6)so increase in sum is by 5380-5050=330.

#### kumar_sarma2000 Profile Answers by kumar_sarma2000 Questions by kumar_sarma2000

• May 13th, 2007

B is 50% faster than A. If A starts at 9 A.M. and B starts at 10 A.M. A travels at a speed of 50 km/hr. If A and B are 300 kms apart, The time when they meet when they travel in opposite direction is Ans:12 noon

speed of A=50 so speed of B=75.

let at T am they meet.

so distance travelled by A=50(T-9)
abd distance by B=75(T-10).

total=50(T-9)+75(T-10)=300 so T=12 noon.

#### kumar_sarma2000 Profile Answers by kumar_sarma2000 Questions by kumar_sarma2000

• May 13th, 2007

A,B,C, can do a work in 8,14,16 days respectively. A does the work for 2 days. B continues from it and finishes till 25% of the remaining work. C finishes the remaining work. How many days would have taken to complete the work Ans:

A compltes 1/4th in 2 days and remaining is 3/4th.
B completes 3/16 th work in 14*3/16 21/8 days
C completes 9/16 th work in 9 days. so total no of days =2+21/8+9=13 5/8 days.

#### arun

• Sep 26th, 2007

80 coins.
Ans: 6
1st time: 40 coins in each. weigh them.
Hence 20 coins remain. continue in this manner. until 5 coins remain.
then place 2 coins in each.

#### abhideepbakshi

• Oct 2nd, 2007

The problem may be solve in this way also .
A travel =50km/hr.
b travel=50 + 50*50/100.=75km/h.
Let x be the distance travel, after that they meet.
then x be the distance travel by A in time t1.
& the same x distance is travel by B in time t2.
then there time ratio is,
t1:t2=x/50:x/75=3:2.

Therefore if A travel x distance in time 3 hour & same distance travel by B
in 2 hour.
so, A start at 9AM+3=12 noon & B start at 10AM+2=12noon.
so they meet at 12 noon.

#### jayath419 Profile Answers by jayath419

• Jan 7th, 2008

shouldnt the answer fer coins b 7???????

#### jayath419 Profile Answers by jayath419

• Jan 7th, 2008

srry 6 is rite!!!!

#### Gagan159 Profile Answers by Gagan159

• Jan 18th, 2008

question no12 ans 9.00pm

#### karthik I Profile Answers by karthik I

• May 22nd, 2008

12. A starts at 11:00AM and travels at a speed of 4km/hr. B starts at 1:00PM and travels at 1km/hr for the first 1hr and 2km/hr for the next hr and so on. At what time they will meet each other.

#### sugankcg Profile Answers by sugankcg

• Jun 9th, 2008

22)this is true when B is negative

#### divyav Profile Answers by divyav

• Jun 14th, 2008

divya: Let Fathers age and sons age be 5x and 3x respectively
then, Fathers age after 10 years= (5x+10)
Son's age after 10 years =(3x+10)
(5x+10)/(3x+10)=3/2
2(5x+10)=3(3x+10)
x=10
father's age is 50
son's age is 30

#### pushpa1989 Profile Answers by pushpa1989

• Jul 18th, 2008

ans for question no 30 is 32

#### arunachalamit Profile Answers by arunachalamit

• Aug 31st, 2008

Split the coins into 3 groups
27, 27, 26

1) measure 27 & 27..
if equal the coin is in the remaining 26,
else it must be in any one of the 27.

2) 9,9,9

3) 3,3,3

4) 1,1,1

#### amitsedai Profile Answers by amitsedai

• Mar 7th, 2009

80 coins - One Counterfeit-  No of weighings required.

Step 1:  Divide 80 as : 27 -  27- 26 : If the first two weighing are the same select 26 coins later.

Step 2:  Taking the worst case: 27
Divide into 3 groups : 9 -9-9

Step 3: Divide 9 as : 3-3-3

Step 4: Divide 3 as 1-1-1

The logic is: On weighing 1 and 1 , if one one tilts you know, which coin is counterfeit, else the remaining one coin is counterfeit.

#### amitsedai Profile Answers by amitsedai

• Mar 7th, 2009

Question:
How will you find distance between Nagpur and Mumbai? I took one hour more when I travel at 80 km/hr than at 90 km/hr.

Distance = Speed x Time

Hence ,
Distance = 80 x (t +1 )  --(1), since it takes one hour more

Distance  =  90 x t -- (2), where t is the time in hours, since speed (given)  also has dimensions in hours.

Now, dividing one by the other.  Since distance is the same , it will result to 1, hence you get the equation after solving:

t= 8

On solving for both the equations above, you get the distance as: 720 Kms.

#### amitsedai Profile Answers by amitsedai

• Mar 7th, 2009

26. A car travels from B at a speed of 20 km/hr. The bus travel starts from A at a time of 6 A.M. There is a bus for every half an hour interval. The car starts at 12 noon. Each bus travels at a speed of 25 km/hr. Distance between A and B is 100 km. During its journey , The number of buses that the car encounter is

The car encounters the first bus when it starts, or in some mins if car starts earlier :)

The car travels slower than any bus , as given in the question, hence it will not be able to catch up with the other buses which had left before.

Distance = Speed x time. The car takes 5 hours to reach the destination. Buses take 4 hours.

Hence the bus which will start 30 minutes or 1 hour later than the car will be able to catch up with the car.

Hence the total no. of buses encountered is: 3

#### amitsedai Profile Answers by amitsedai

• Mar 7th, 2009

If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by Ans: 330

Another way of looking at this question is where all do we need to replace:

Exluding 60 - 69 , we are left with 9 places 6, 16,26,36,46,56,76,86,96 where adding 3 each will make the changes, hence partial sum now is 9 x 3 =27.

In the remaining part: excluding 66, 60 - 69 can to be replaced  by adding 30 , which comes as 30 x 9 =270 .

Finally , for 66 adding 33 will suffice.

Hence the difference will be:

27 + 270 +33 =   330

#### arunkumar6600 Profile Answers by arunkumar6600

• Nov 28th, 2009

There will be 51 multiples of 2 between 100 and 200 (both are inclusive)
There will be 33 mutiples of 3 between 100 and 200 (both are inclusive)
Number of mutiples in common is 17
(51+33)-17 = 67
Its just logical just think cool.

#### shikhachordia Profile Answers by shikhachordia

• Feb 4th, 2010

90 x n=80 x (n+1)
=> n=8
so distance =90 x 8=720km

Answer for 12th Question is 7
Method-Let it take n hours
when they meet the distance travelled by both shud be same.
so 4*n=n(n+1)/2n=7

Answer for 27th Question - Father's age will be-60 and son's age will be 40

Answer for 22nd Question - It can hold true for both condtions.he main  thing is that the value of C>B

Answer 19th Question - They will take 40 seconds

Answer 15th Question - 13.55 days

#### veena selvam Profile Answers by veena selvam Questions by veena selvam

• Feb 18th, 2010

Question 3:

From a pack of cards Jack, Queen, King & ace are removed. Then the algebraic sum of rest of the cards is

A pack of cards has 52 cards.
King = 4
Queen = 4
Jack =  4
Ace = 4
Remaining cards will be from 2 to 10 individually in all the four symbols(spade, diamond, autin,claver)
Sum of numbers from 2 to 10 is
n/2(first digit+last digit)
so, 9/2(2+10)=54
one symbol=54
Four symbol= 54*4 = 216.

#### priyacse068 Profile Answers by priyacse068

• Jul 13th, 2010

The total no divisible by 2 b/w 100 and 200 is 50(102,104....)
The total no divisible by 3 b/w 100 and 200 is 29(120-150 is 10 then 151-180 is 10 then 181-200 is 6)
so total is 79.

#### varunn Profile Answers by varunn

• Aug 5th, 2010

1. Amount of work completed by A in 2 days:1/4
2. B completes half of the work in:7 days
3. Remaining 25% ie 1/4 work is completed by C in 4 days
Therefore no. of days to complete the work=2+7+4=13days

#### prajapatiharibabu Profile Answers by prajapatiharibabu

• Sep 21st, 2010

Total = 80 coins

1 time - 40 + 40

2 time - 20 + 20

3 time - 10 + 10

4 time - 5 + 5

5 time - 2 + 2 here odd coin found no need to further weighing those coins.

#### saurangsu Profile Answers by saurangsu

• Oct 1st, 2010

There is a simpler way of doing it.

The numbers that are changed in two ways:

i) 6 becomes 9, 16, becomes 19, 26 becomes 29....so on.... total 10 changes.

Now for all the changes of the above mentioned type.. the difference is always 3.

For eg. 9-6=3, 19-16=3... so on.... So the total variation due to this type of change is 3*10=30

Now coming to the second type of change
ii) all the digits in the 60s becomes corresponding digits in 90s.

Like 60 becomes 90, 61 becomes 91..and so on... here also the number of changes will be 10 and the variation due to this change will be 30 for each change.

So the total amount of change = 10*30=300

So adding the two up we get 300+30=330

Hope this helps.

#### jyothsna

• Jan 2nd, 2012

Step 1 : weigh 27,27 and 26 coins are left
Step 2 : if one 27 measure less, weigh 9, 9 and 9 is left
Step 3 : weigh 3, 3 and 3 is left
Step 4 : weigh 1, 1 and 1 is left.

but we have to check whether odd coin is in 26 coins which is left.
therefore...

Step 2 : weigh 9, 9 and 8 is left
Step 3 : weigh 3, 3 and 2 is left (if odd coin is in 8 coins which is left)
Step 4 : weigh 1, 1 and 2 is left(if odd coin is in 2 coins which is left)
Step 5 : weigh 1, 1  