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This mock test of SSC CPO Mock Test (Quant Apt) 6 for SSC helps you for every SSC entrance exam.
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QUESTION: 1

The ratio between the ages of P and Q four yrs ago was 5 : 6. If the total of their ages at present is 52 yrs, what is the ratio of their present ages?

Solution:

QUESTION: 2

If x + y = 6 and 3x - y = 4, then x - y is equal to

Solution:

x + y = 6

⇒ y = 6 - x

Now, 3x - y = 4

or 3x - (6 - x) = 4

or 3x - 6 + x = 4

or 4x = 10

QUESTION: 3

A train starts with full of passenges.At the first station,the train drops one-third of the passengers and takes in 96 more.At the next station,one half of the passengers on board get down while 12 new passengers get on board.The number of passengers now is 240.The number of passengers in the beginning was

Solution:

Let the number of passengers be x when the train started off

∴ At the first station, the number of passengers = x - x/3 + 96 = 2x/3 + 96

At the second station, the number of passengers = ( 2x/3 + 96) 1/2 + 12

At the third station, the number of passengers left = x/3 + 48 + 12 = 240

⇒ x/3 = 180

⇒ x = 540

QUESTION: 4

If (2x+3) and (x-1) are two factors of (2x^{2} + x)^{2} - 4(2x^{2} + x) + 3, then the remaining two factors are

Solution:
(2x^{2} + x)^{2} - 4(2x^{2} + x) + 3

= 4x^{4} + x^{2} + 4x^{3} - 8x^{2} - 4x + 3

= 4x^{4} + 4x^{3} - 7x^{2} - 4x + 3

= 4x^{3} (x - 1) + 8x^{2} (x - 1) + x (x - 1) - 3 (x - 1)

= (x - 1) (4x^{3} + 8x^{2} + x - 3)

= (x - 1) [2x^{2} (2x + 3) + x(2x + 3) - 1(2x + 3)]

= (x - 1) (2x + 3) (2x^{2} + x - 1)

= (x - 1) (2x + 3) [2x^{2} + 2x - x - 1]

= (x - 1) (2x + 3) [(2x (x + 1)) - 1(x + 1)]

= (x - 1) (2x + 3) (x + 1) (2x - 1)

= 4x

= 4x

= 4x

= (x - 1) (4x

= (x - 1) [2x

= (x - 1) (2x + 3) (2x

= (x - 1) (2x + 3) [2x

= (x - 1) (2x + 3) [(2x (x + 1)) - 1(x + 1)]

= (x - 1) (2x + 3) (x + 1) (2x - 1)

QUESTION: 5

Total number of boys and girls eligible for the book grant is 9. Each boy is given a grant of Rs 25 and each girl Rs 20. If the total amount given as grant is Rs 200,the number of girls eligible for grant is

Solution:

QUESTION: 6

A company produces on an average 4000 items per month for the first 3 months. How many items it must produce on an average per month over the next 9 months, to average 4375 items per month over the whole?

Solution:

∴ 4500 items per month should be produced for the last 9 months

QUESTION: 7

Diagonals of a rhombus are in the ratio 3:4 and its area is 2400 cm^{2}. Side of the rhombus is

Solution:

Let the diagonals of a rhombus are 3K and 4K. Then

Area of rhombus = 1/2 x product of diagonals

2400 = 1/2 x 3K x 4K

or 400 = K^{2}

or K = 200

∴ The Diagonals are 60 cm and 80 cm

we know that, if a be side of the rhombus and AC and BD be its diagonals then

(AC)^{2} + (BD)^{2} = 4 x a^{2}

or (60)^{2} + (80)^{2} = 4 x a^{2}

or 3600 + 6400 = 4 x a^{2}

or 10000 = 4a^{2}

or 2500 = a^{2}

or a = 50 cm

QUESTION: 8

A rectangular park is 200 by 150m. Two cross paths are to be made one parallel to the length and the other parallel to the breadth. The longer path is to be 3 m wide and the shorter is to be 2 m wide. The cost of grassing the remaining part of the park @ Rs. 1000 per ha is

Solution:

Area of the park minus the paths

= (200 - 3) (150 - 2)

= 197 × 147 sq. m

= 29156 sq. m

The cost of grashing the remaming part of the park = Rs 29156/10000 x 1000

= Rs 2915.6

QUESTION: 9

The area of the sector of the circle is 1/10th the area of the circle. The angle of the sector is

Solution:

QUESTION: 10

The average of 50 numbers is 30. If two numbers, 35 ad 40 are discarded, then the average of the remaining numbers is nearly:

Solution:

Sum of 50 number = 30 x 50 = 1,500

Sum of remaining 48 numbers = 1,500 - (35 + 40) = 1,425

QUESTION: 11

If the equation 12x² + 7xy - py² - 18x + y + 6 = 0 represents a pair of perpendicular lines, then

Solution:

QUESTION: 12

At what per cent annum will Rs 3000 amount to Rs 3993 in 3 years if the interest is compounded annually?

Solution:

QUESTION: 13

is equal to

Solution:

QUESTION: 14

The marked price of a watch was Rs 720. A man bought the same for Rs 550.80 after getting two successive discounts,the first being 10%. What was the second discount rate?

Solution:

QUESTION: 15

Two-third of a positive number and 25/216 of its reciprocal are equal. The number is

Solution:

QUESTION: 16

AB∥CD and P is a point between the lines, the measure of the angles ∠ABP+∠BPD+∠CDP is

Solution:

QUESTION: 17

Statement-"A curve is always a locus but a locus need not be a curve." The statement is

Solution:

QUESTION: 18

Radius of a circle is 61 cm. If a chord of a this circle is 11 cm from the centre then the length of the chord is

Solution:
Using Pythograrous theorem as in above MB = 60 cm so length of chord = 120 cm.

QUESTION: 19

Lines AB and CD intersect at O. This forms four angles. If sum of three of these is 299° then the measure of the fourth angle is

Solution:

Sum of all angles about a point is 360

299 + x = 360°

so, x = 61

QUESTION: 20

Find the least multiple of 23,which when divided by 18,21 and 24 leaves the remainders 7,10 and 13 respectively.

Solution:

QUESTION: 21

A light house is 60 metres high with its base being at the sea level.If the angle of depression of a boat in the sea from the top of the light house is 15°,then the distance of the boat from the foot of the light house is equal to

Solution:

QUESTION: 22

The sum of the two digits number is 15. If 9 be added to the number, then the digits are reversed. The number is

Solution:

QUESTION: 23

A district has 64000 inhabitants. If the population increases at the rate of 2(1/2)% per annum, then the number of inhabitants at the end of 3 years will be

Solution:

QUESTION: 24

In a school 70% of the students are girls. The number of boys is 510. Then the total number of students in the school is

Solution:

QUESTION: 25

A tap can fill a tank in one hour. A second tap empty it in 30 minutes. If both the taps operate simultaneously, how much time is needed to empty the tank?

Solution:

In one minute 1/60 + 1/30 = 1/20 of the tank will be empty

QUESTION: 26

A book-seller bought 200 textbooks for Rs 12,000. He wanted to sell them at a profit so that he got 20 books free. At what profit percent should he sell them?

Solution:

QUESTION: 27

Kewal sells two tape recorders at the same price. On one,he gains 10% and on the other, he loses 10%. The total gain or loss in the transaction is

Solution:

QUESTION: 28

In a triangle AC, if a = 2, B = 60° and c = 75°, then b =

Solution:

QUESTION: 29

The ratio between the present ages of P and Q is 3:4 respectively. If P's age is 20 yrs,what will be the ratio of their ages after 5 yrs?

Solution:

QUESTION: 30

Rs 6400 are divided among three workers in the ratio . The share of the second worker (in rupees)is

Solution:

QUESTION: 31

If 4th term of an H.P. is 5 and 5th term is 4, then its 20th term is

Solution:

QUESTION: 32

The interest on Rs 4500 from January 5 to May 31, 1954 at 8% is

Solution:

QUESTION: 33

The square root of 0.09 + 2x0.21 + 0.49 is

Solution:

QUESTION: 34

A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 47 minutes. The total distance (in km) is:

Solution:

QUESTION: 35

12 women complete a work in 20 days. If only 8 women are employed, the time required to complete the same work is

Solution:

QUESTION: 36

cotx - tanx =

Solution:

QUESTION: 37

sin 20° sin 40° sin 60° sin 80°=

Solution:

QUESTION: 38

[(sinθ+sin2θ)/(1+cosθ+cos2θ)]=

Solution:

QUESTION: 39

A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm. The height of the cone is :

Solution:

QUESTION: 40

A cube of edges 5 cm is cut into cubes each of edge 1 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to :

Solution:

QUESTION: 41

The radii of two right circular cylinder are in ratio 2: 3 and their heights are in ratio 5:4. The ratio of their curved surface areas is

Solution:

QUESTION: 42

**Study the following graph showing the sales forecast for the next ten weeks, to answer these questions.**

**Q. **If the forecasted demand is met by having uniform production during the weeks at an average level, then the number of weeks during which demand will not be met is :

Solution:

Average sales forecast for 10 weeks = 322

Hence there are 4 weeks during which demand will not be met

QUESTION: 43

**Study the following graph showing the sales forecast for the next ten weeks, to answer these questions.**

**Q. **If the production is uniform, then what should be the minimum capacity of the storage space to store the units in excess of demand?.

Solution:

QUESTION: 44

**Study the following graph showing the sales forecast for the next ten weeks, to answer these questions.**

**Q. **If the maximum production capacity is 300 units, then the demand that will not be met will be

Solution:

unmet demand = 475 - 300 = 175

QUESTION: 45

**Q. **During which year was the percentage rise/fall in sales from the previous year the higest for company A ?

Solution:

QUESTION: 46

**The following questions are based on the following pie chart which gives the expenditure incurred in printing a magazine.**

**Q. **What is the angle for the sector representing paper cost ?

Solution:

Angle for sector representing paper cost = 360/100 × 10 = 36°

QUESTION: 47

**The following questions are based on the following pie chart which gives the expenditure incurred in printing a magazine.**

**Q. **What should be the central angle of the sector representing transportation charges ?

Solution:

Angle for sector representing transportation = 360/100× 4 = 14.4°

QUESTION: 48

**The following questions are based on the following pie chart which gives the expenditure incurred in printing a magazine.**

**Q. **If the editorial contents development cost is Rs.30,000, then the cost of transportation can be expected to be

Solution:

30% = 30,000

1% = 1000

∴ 4% = Rs 4000

QUESTION: 49

**Q. **For a given issue of the magazine , the miscellaneous cost is Rs.2000 and the print-run is 12500 copies. What should be the sale price if the publisher desires a profit of 5% ?

Solution:

QUESTION: 50

**Q. **If for the same data as given in the previous question , the print-run were to be 50000 copies , the sale price per copy would have been :

Solution:

Cost price per copy = 100000/50000 = Rs 2

SP at a profit of 5%

SP = 2 × 1.05 = Rs 2.10

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