A candidate with **quantitative aptitude** knowledge will be in a better position to analyse and make sense of the given data. Quantitative Aptitude knowledge is an **important** measure for a prospective business executive’s **abilities**.

The article **SSC CPO Quantitative Aptitude Quiz 18** provides Quantitative Aptitude questions with answers useful to the candidates preparing for** Competitive exams, Entrance exams, Interviews** etc. The article **SSC CPO Quantitative Aptitude Quiz 18** will assist the students to know the expected questions from **Quantitative Aptitude**.

- A. 48

B. 42

C. 28

D. 36

**Answer**: Option B

**Explanation**:

First, we find out the number of times a particular letter occurs in the given word:

2 – I

1 – A

1 – D

1 – N

=> Total number of solutions minus the number of times all three vowels are together.

Now, using the concept of permutation and combination:

=> Divide the possible combination by 2! because it occurs twice and replacing one by another will cause no difference in the word.

=> Total number of words that can be formed: 5!/2!

=> Total number of words that can be formed keeping all the vowels together: 3! 3!/2!

=> 60 – 18 = 42

**2. The income of A is 25% more than the income of B. What is the income of B in terms of income of A?**

- A. 80%

B. 75%

C. 78.66%

D. 71.25%

**Answer**: Option D

**Explanation**:

One of the most basic questions.

Let the income of B be 100. The income of A is 25% more than the income of B which means Income of A becomes 125

Now income of B in terms of A = 100/125 *100 = 80%

**3. A starts walking at 4 kmph and 4 hours after his start B starts cycling at 10 kmph. After how much distance will B catch up with A?**

- A. 26.2 km

B. 25.7 km

C. 23.2 km

D. 26.67 km

**Answer**: Option D

**Explanation**:

Distance travelled by each of them is to be made equal.

=> Distance traveled walking = Distance covered cycling.

Let after 4 hours of walking, A walk for x hours more before B catches up with him.

=> Distance = Speed * Time

(4+x)4 = 10x

x = 8/3

Therefore, It takes B 8/3 hours to catch up with A. Distance: 8/3 x 10 = 80/3 km = 26.67

**4. If one is added to the numerator of the fraction it becomes one. If one is added to the denominator of the fraction it becomes 1/2. The fraction is?**

- A. \(\frac{1}{2}\)

B. \(\frac{3}{5}\)

C. \(\frac{2}{3}\)

D. \(\frac{2}{5 }\)

**Answer**: Option C

**Explanation**:

Let the fraction be \(\frac{X}{Y }\).

=> \(\frac{X + 1}{Y}\) = 1

=> x+1 = y—(1)

\(\frac{X}{Y – 1 }\) = \(\frac{1}{2 }\)

=> 2x = (y+1)—(2)

=>Equating (1) and (2)

=> x+1 = 2x-1

=>x=2

Substituting the value of x in (1)

=>y=3

=>2/3

**5. A boat with speed 15 km/hr in standing water goes 30 km downstream and returns in a total of 4.5 hours. What is the speed of current?**

- A. 4 kmph

B. 6 kmph

C. 5 kmph

D. 8 kmph

**Answer**: Option C

**Explanation**:

Speed of the boat in still water: 15 km/hr

Speed of boat downstream: (15+x)km/hr where x is the speed of the current.

The boat travels 30 km downstream and then 30 km upstream and takes \(\frac{9}{2 }\) hours.

Total time= Time taken to travel downstream + Time is taken to travel upstream

=> 4/5= (30/(15+x))+(30/(15-x))

=>x= 5

- A. 88

B. 106

C. 125

D. 76

**Answer**: Option A

**Explanation**:

This sequence represents a series in which from the reverse order a prime number is added:

53+5=58

58+7=65

65+11=76

76+13=89

89+17=106

106 + 19 = 125

Hence 88 is the answer.

**2. What is the CP of Rs 100 stock at 4 discount, with 1/5% brokerage?**

- A. 99.6

B. 96.2

C. 97.5

D. 98.25

**Answer**: Option B

**Explanation**:

Use the formula,

CP= 100 – discount + brokerage%

CP= 100 – 4 +\(\frac{1}{5 }\)

96.2

Thus the CP is Rs 96.2.

**3. A pipe is 30 m long and is 45% longer than another pipe. Find the length of the other pipe.**

- A. 20.68

B. 20

C. 20.12

D. 20.5

**Answer**: Option B

**Explanation**:

Let length of other pipe be X

According to question,

30 = \(\frac{45}{100 }\) X + X

30 = 0.45X + X

30 = 1.45 X

X= \(\frac{30}{1.45 }\)

X = 20.68m

Thus the length of the other pipe is 20.68 meters.

**4. 15th august 2010 was which day of the week?**

- A. Thursday

B. Friday

C. Wednesday

D. Sunday

**Answer**: Option D

**Explanation**:

15th August 2010 can be written as 2009 + days from 1st January 2010 to 15th August 2010.

=> Total number of odd days in 400 years = 0

Hence, the total number of odd days in 2000 years = 0 (as 2000 is a perfect multiple of 400)

Odd in days in the period 2001-2009:

7 normal years + 2 leap yeas

=> (7*1) + (2*2) = 11

=> Odd days will be 11- (7*1) = 4

Days from January 1 to August 15 in 2010: 31+28+31+30+31+30+31+15

= 227 days.

= 32 weeks and 3 days, this gives additional 3 odd days.

=> Total odd days= 3+4=7

=> 7 odd days=1 week= 0 odd days

=> 0 odd days= Sunday

Thus, 15th August 2010 was a Sunday.

**5. A boatman rows 96 km downstream in 8 hours with a stream speed of 4kmph. How much time will he take to cover 8km upstream?**

- A. 4 hours

B. 6 hours

C. 2 hours

D. 1 hours

**Answer**: Option C

**Explanation**:

Speed = distance/time

Speed downstream: \(\frac{96}{8 }\) km/hr = 12kmph

Speed of stream = 4kmph

Effective speed of boat = (12-4) kmph

= 8kmph

Distance to be traveled upstream= 8 km

Speed upstream = boat speed-current speed

= 8-4 kmph

= 4 kmph

Time taken = \(\frac{Distance}{Speed }\) = \(\frac{8}{4 }\) hours

= 2 hours

Thus it will take 2 hours to go upstream.

- A. 4.04

B. 4

C. 40.4

D. 4.004

** Answer**: Option A

**Explanation**:

Given Error = 2% while measuring the side of a square.

If the correct value of the side of the square is 100, the measured value:

=> 100 + 2% *100

= 100+2=102

The area of a square with edge 100 = side*side

=> 100*100

=> 10000

The area of a square with side 102 = 102*102= 10404

Error in area calculation = 10404-1000 = 404

% error= \(\frac{404}{10000 }\)*100

= 4.04%

**2. Akash and Akshay are business partners. Akash invests Rs 35,000 for a period of 8 months and Akshay invests Rs 42,000 for a period of 10 months. Out of a total profit of Rs 31,570 what is Akash’s share?**

- A. Rs 12,420

B. Rs 18,040

C. Rs 18,942

D. Rs 12,628

** Answer**: Option D

**Explanation**:

For a given business profit is directly dependent upon the capital invested and the time of investment.

=> Ratio of shares of Akash and Akshay becomes: (35,000*8)/(42,000*10) = \(\frac{2}{3 }\)

=>% of profit belonging to Akash: \(\frac{2}{3 + 2 }\)*(31,570)

=>Rs 12,768

**3. In what ratio must one add water to milk so as to gain 16.666% on the selling this mixture at the cost price?**

- A. 1:6

B. 1:3

C. 6:1

D. 3:1

** Answer**: Option A

**Explanation**:

To start off this question let us assume that cost price of 1 litre milk is Rs 1

No need to make a mixture and sell this mixture at 1 Rs per liter such that the total gain on the mixture is 16.667%.

Therefore, CP of 1 liter of the mixture becomes (quantity of milk)/ (quantity of mixture containing 1 L milk)*(the price of 1-liter milk).

=>\(\frac{(100}{(100+50/3) }\)*1

=>CP of 1-litre milk of mixture: Rs \(\frac{5}{6 }\)

As the price of any amount of water is zero, and as 1-liter milk costs Rs 1.5/6litre of the mixture will comprise entirely of cost of milk which means,1 liter of the mixture will

contain 5/6th amount of milk.

=>Water is added in the ratio of (1-\(\frac{5}{6 }\))= \(\frac{1}{6 }\)

**4. Ram can finish a puzzle in 3 hours and Shyam can do the same in 2 hours. Both of them finish the puzzle and get 15 candies. What is Ram’s share?**

- A. 3

B. 6

C. 11

D. 12

** Answer**: Option B

**Explanation**:

The question is based on efficiency to do work.

Ram can finish a puzzle in 3 hours. Shyam can finish the puzzle in 2 hours.

=>In one hour Ram can finish 1/3rd of a puzzle

=>In one hour Shyam can finish half the puzzle

A total of 15 candies are to be shared amongst both of them

Hence Ram’s share must be = ((Work done by Ram in 1 hour)/(Work is done by Shyam in one hour)+(Work done by Ram in an hour))*15

=> 1/3/((1/2)+(1/3))*15

=> (1/3/(5/6))*15

=> \(\frac{6}{15 }\)*(15)

=>6 candies

**5. A man sells 45 lemons for Rs 40 and loses 20%. At how much price should he sell 24 lemons to the next customer to make a 20% profit?**

- 32

B. 20

C. 24

D. 16

** Answer**: Option A

**Explanation**:

Let cost price of lemons be x.

Selling price of lemons becomes CP – loss.

=>SP=x-(20/100)x

=>40=x(80/100)

=>50

So 45 lemons cost Rs 50

Cost of 1 lemon = \(\frac{50}{45 }\) Rs

Cost of 24 lemons = (\(\frac{50}{45}\))*24 =80/3 Rs

Selling Price of 24 lemons = (\(\frac{80}{3 }\))+(\(\frac{20}{100 }\))(\(\frac{80}{3 }\))=Rs 32