# QUANTITATIVE APTITUDE ( SSC FCI Assistant Grade-III Exam, 07-04-2013 - Previous Year Paper )

**Quantitative Aptitude** || English Comprehension

### QUANTITATIVE APTITUDE

- If tan θ + cot θ = 2, then the value of tan
^{100}θ + cot^{100}θ is

(1) 2

(2) 0

(3) 1

(4) √3### Show Answer

**Solution:1**

- The angles of elevation of the top of a tower from the points P and Q at distances of 'a' and `b' respectively from the' base of the tower and in the same straight line with it are complementary. The height of the tower is

### Show Answer

**Solution:1**

- The value of
(1) 8

(2) 1

(3) √2

(4) 0### Show Answer

**Solution:4**

- The area (in sq. unit) of the triangle formed in the first quadrant by the line

3x + 4y = 12 is

(1) 8

(2) 12

(3) 6

(4) 4### Show Answer

**Solution:3**

- If A and B are the H.C.F. and L.C.M. respectively of two algebraic expressions x and y, and A + B = x + y, then the value of A
^{3}+ B^{3}is

(1)x^{3}— y^{3}

(2) x^{3}

(3) y^{3}

(4) x^{3}+ y^{3 }### Show Answer

**Solution:4**

(1) 764

(2) 750

(3) 756

(4) 760### Show Answer

**Solution:3**

(1) 2√3

(2) 2

(3) 3√3

(4) 0### Show Answer

**Solution:4**

- If the internal bisectors of the ∠ABC and ∠ACB of ΔABC meet at 0 and also ∠BAC = 80°, then ∠BOC is equal to

(1) 50°

(2) 160°

(3) 40°

(4) 130°### Show Answer

**Solution:4**

- O is the in-centre of the ΔABC, if ∠BOC = 116°, then ∠BAC is

(1) 42°

(2) 62°

(3) 58°

(4) 52°### Show Answer

**Solution:4**

- The area of the circumcircle of an equilateral triangle is 3π sq. cm. The perimeter of the triangle is

(1) 3√3 cm

(2) 9 cm

(3) 18 cm

(4) 3 cm### Show Answer

**Solution:2**

- In ΔABC, ∠A = 90° and AD ⊥ BC where D lies on BC. If BC =8 cm, AC = 6 cm, then ΔABC : ΔACD =?

(1) 4 : 3

(2) 25 : 16

(3) 16 : 9

(4) 25 : 9### Show Answer

**Solution:3**

- Inside a triangle ABC, a straight line parallel to BC intersects AB and AC at the points P and Q respectively. If AB = 3 PB, then PQ : BC is

(1) 1 : 3

(2) 3 : 4

(3) 1 : 2

(4) 2 : 3### Show Answer

**Solution:4**

- There are 50 boxes and 50 persons. Person 1 keeps 1 marble in every box. Person 2 keeps 2 marbles in every 2nd box, person 3 keeps 3 marbles in every third box. This process goes on till person 50 keeps 50 marbles in the 50th box. Find the total number of marbles kept in the 50th box.

(1) 43

(2) 78

(3) 6

(4) 93### Show Answer

**Solution:4**

- 252 m of pant cloth and 141 m of shirt cloth are available in a cloth store. To stitch one pant and one shirt, 2.5 m and 1.75 m of cloth are needed respectively. Then the approximate number of pants and shirts that can be made out of it are

(1) (80,100)

(2) (100,80)

(3) (100,90)

(4) (90,80)### Show Answer

**Solution:1**

- The greatest nummber that divides 411, 684, 821 and leaves 3, 4 and 5 as remainders, respectively, is

(1) 254

(2) 146

(3) 136

(4) 204### Show Answer

**Solution:3**

(1) 3√3

(2) 4

(3) 7

(4) 2,5### Show Answer

**Solution:2**

- Terms a, 1, b are in Arithmetic Progression and terms 1, a, b are in Geometric Progression. Find `a' and `b' given a # b.

(1) 2,4

(2) -2, 1

(3) 4,1

(4) -2, 4### Show Answer

**Solution:4**

- There are two groups A and B of a class, consisting of 42 and 28 students respectively. If the average weight of group A is 25 kg and that of group B is 40 kg, find the average weight of the whole class.

(1) 69

(2) 31

(3) 70

(4) 30### Show Answer

**Solution:2**

- The average monthly salary of all the employees in an industry is 12,000. The average salary of male employees is 15,000 and that of female employees is 8,000. What is the ratio of male employees to female employees ?

(1) 5 : 2

(2) 3 : 4

(3) 4 : 3

(4) 2 : 5### Show Answer

**Solution:3**

- Arun marks up the computer he is selling by 20% profit and sells them at a discount of 15%. Arun's net gain percent is

(1) 4

(2) 2

(3) 3.5

(4) 2.5### Show Answer

**Solution:2**

- A dealer buys a table listed at 1,500 and gets successive discounts of 20% and 10%. He spends 20 on transportation and sells at a profit of 20%. Find the Selling Price of the table (in rupees).

(1) 1320

(2) 1080

(3) 1200

(4) 1230### Show Answer

**Solution:1**

- A sells an article to B at a gain of 20% and B sells it to C at a gain of 10% and C sells it to D at a gain of 12.5 %. If D pays 29.70, A purchased the article for

(1) 40

(2) 10

(3) 20

(4) 30### Show Answer

**Solution:3**

- By selling 80 ball pens for 140 a retailer loses 30%. How many ball pens should he sell for 2104 so as to make a profit of 30%?

(1) 32

(2) 52

(3) 48

(4) 42### Show Answer

**Solution:1**

- Nitin borrowed some money at the rate of 6% p.a. for the first three years, n p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is 8,160, the money borrowed by him (in ) was

(1) 12,000

(2) 6,000

(3) 8,000

(4) 10,000### Show Answer

**Solution:3**

- A boy started from his house by bicycle at 10 a.m. at a speed of 12 km per hour. His elder brother started after 1 hr 15 mins by scooter along the same path and caught him at 1.30 p.m. The speed of the scooter will be (in km/hr)

### Show Answer

**Solution:3**

- Two pipes A and B can fill a cistern in 3 hours and 5 hours respectively. Pipe C can empty in 2 hours. If all the three pipes are open, in how many hours the cistern will be full?

(1) can't be filled

(2) 10 hours

(3) 15 hours

(4) 30 hours### Show Answer

**Solution:4**

- Two men can do a piece of work in x days. But y women can do that in 3 days. Then the ratio of the work done by 1 man and 1 woman is

(1) 3y : 2x

(2) 2.x : 3y

(3) x : y

(4) 2y : 3x### Show Answer

**Solution:1**

- A clerk received as annual salary of 3,660 in the year 1975. This was 20% more than his salary in 1974. What was his salary in 1974 ?

(1) 3,005

(2) 3,000

(3) 3,500

(4) 3,050### Show Answer

**Solution:4**

- Out of his total income, Mr. Kapur spends 20% on house rent and 70% of the rest on house-hold expenses. If he saves 1,800, what is his total income (in rupees)?

(1) 7,800

(2) 7,000

(3) 8,000

(4) 7,500### Show Answer

**Solution:4**

- The sides of a triangle are in the ratio 1/4 : 1/6 : 1/8 and its perimeter is 91 cm. The difference of the length of longest side and that of shortest side is

(1) 19

(2) 20

(3) 28

(4) 21### Show Answer

**Solution:4**

- A box contains 56 in the form of coins of one rupee, 50 paise and 25 paise. The number of 50 paise coins is double the number of 25 paise coins and four times the number of one rupee coins. How many 50 paise coins are there in the box?

(1) 52

(2) 64

(3) 32

(4) 16### Show Answer

**Solution:2**

- The perimeter of an isosceles right angled triangle is 2p cm. Its area is

### Show Answer

**Solution:2**

- The ratio between the areas of two circles are 4 : 7. What will be the ratio of their radii?

(1) 2 : √7

(2) 4 : 7

(3) 16 : 49

(4) 4 : √7### Show Answer

**Solution:1**

- The perimeter of a non-square rhombus is 20 cm. One of its diagonal is 8 cm. The area of the rhombus is

(1)28 sq cm

(2) 20 sq cm

(3)22 sq cm

(4) 24 sq cm### Show Answer

**Solution:4** - If each edge of a cube is increased by 50%, the percentage increase in its surface area is

(1) 150%

(2) 75%

(3) 100%

(4) 125%### Show Answer

**Solution:4**

- The diameter of a copper sphere is 1 8 cm. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 108 m, the diameter of the wire is

(1) 1 cm

(2) 0.9 cm

(3) 0.3 cm

(4) 0.6 cm### Show Answer

**Solution:4**

- A semicircular sheet of metal of diameter 28 cm is bent into an open conical cup. The capacity of the cup

(1) 624.26 cm^{3}

(2) 622.26 cm^{3}

(3) 622.56 cm^{3}

(4) 623.20 cm^{3 }### Show Answer

**Solution:2**

- If surface area and volume of a sphere are S and V respectively, then value of s
^{2}/v^{2}is

(1) 32 unit

(2) 9 unit

(3) 18 unit

(4) 27 unit### Show Answer

**Solution:**

### Show Answer

**Solution:4**

### Show Answer

**Solution:2**

- The circular measure of an angle of an isosceles triangle is 5π/9 . Circular measure of

one of the other angles

### Show Answer

**Solution:3**

**Directions (42 - 45) :**Bar-chart showing the Sales of Books (in 1000) from six-branches B_{1}B_{2}, B_{3}, B_{4}, B_{5}and B_{6}of a Publishing Company in 2000 and 2001 is given below. Study the chart and answer the questions. - Total sales of branch B
_{6}for both the years is what percent of the total sales of branch B_{3}for both the years?

(1) 71.11%

(2) 73.17%

(3) 68.54%

(4) 77.26%### Show Answer

**Solution:2**

- What is the ratio of the total sales of branch B
_{2}for both the years to the totai sales of branch B_{4}for both years ?

(1) 2 : 3

(2) 3 : 5

(3) 5 : 7

(4) 7 : 9### Show Answer

**Solution:4**

- What percent of the average sales of branches B
_{1}, B_{2}and B_{3}in 2001 is the average sales of branches B_{1}, B_{3}and B_{6}in 2000 ?

(1) 87.5%

(2) 75%

(3) 77.5%

(4) 85%### Show Answer

**Solution:**

- What is the average sale of books from all the branches for the year 2000?

(1) 70

(2) 80

(3) 70.5

(4) 80.5### Show Answer

**Solution:2**

**Directions (46-50) :**The pie-chart given below represents the number of students using different transport to a school in which total number of students is 2160.

Answer the questions based on the following diagram. - The number of students who come to school by car is

(1) 70

(2) 290

(3) 420

(4) 480### Show Answer

**Solution:3**

- The ratio of the number of students who come to school by car to the number of students who come to school by bus is

(1) 21 : 24

(2)21 : 27

(3) 36 : 27

(4) 36 : 21### Show Answer

**Solution:2**

- The total number of students coming to school either by walking or by bus is

(1) 180

(2) 540

(3) 1020

(4) 170### Show Answer

**Solution:3**

- The number of students who don't come to school by train is

(1) 720

(2) 1020

(3) 2040

(4) 1440### Show Answer

**Solution:4**

- The number of students coming to school by bus exceeds the number of students coming to school walking, by

(1) 10%

(2) 12.5%

(3) 11%

(4) 11.5%### Show Answer

**Solution:2**