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Quantitative Aptitude  ||  English Comprehension

### QUANTITATIVE APTITUDE

1. A and B can do a job alone in 12 days and 15 days respectively. A starts the work and after 6 days B also joins to finish the work together. For how many days B actually worked on the job ?

Solution :1

2. Two pipes can fill a cistern separately in 24 minutes and 40 minutes respectively. A waste pipe can drain off 30 litres per minute. flail the three pipes are opened, the cistern fills in one hour. The capacity (in litres) of the cistern is
(1) 800
(2) 400
(3) 600
(4) 500

Solution :3

3. A solid sphere of radius 1 cm is melted to convert into a wire of length 100 cm. The radius of the
wire (using √3 = 1.732) is
(1) 0.08 cm
(2) 0.09 cm
(3) 0.16 cm
(4) 0.11 cm

Solution :4

4. A field is in the form of a rectangle of length 18m and width 15 m. A pit, 7.5 m long, 6 m broad and 0.8 m deep, is dug in a corner of the field and the earth taken out is evenly spread over the remaining area of the field. The level of the field raised is
(1) 12 cm
(2) 14 cm
(3) 16 cm
(4) 18 cm

Solution :3

Solution :2

6. The last digit, that is, the digit in the unit’s place of the number I(57)25 – 11 is
(1) 6
(2) 8
(3) 0
(4) 5

Solution :1

7. The sum of five consecutive integers is a and the sum of next five consecutive integers is b.

(1) 0.25
(2) 0.50
(3) 4
(4) 2

Solution :1

8. (1) 1
(2) -√3
(3) √3 + √2
(4) √3 – √2

Solution :2

9. A number N is a positive three-digit number. If x is in its hundred’s place and y is in its unit’s place, then the number N -100x – y is always divisible by
(1) 8
(2) 9
(3) 10
(4) 11

Solution :3

10. A discount of 40% on the marked price of a trouser enables Ajit to purchase a shirt also which costs him Rs. 320. How much did Ajit pay for the trouser ?
(1) Rs. 480
(2) Rs. 540
(3) Rs. 800
(4) Rs. 400

Solution :1

11. The ratio of alcohol and water in 40 litres of mixture is 5 : 3. Then 8 litres of the mixture is removed and replaced with water. Now, the ratio of the alcohol and water in the resultant mixture is
(1) 1 : 2
(2) 1 : 1
(3) 2 : 1
(4) 1 : 3

Solution :2

1. Rama’s expenditure and savings are in the ratio 3 : 2. His income increases by 10 percent. His expenditure also increases by 12%. His savings increases by
(1) 7%
(2) 10%
(3) 9%
(4) 13%

Solution :1

2. Ten years ago the average age of P and Q was 20 years. Average age of P, Q and R is 30 years now. After 10 years, the age of R will be
(1) 35 years
(2) 40 years
(3) 30 years
(4) 45 years

Solution :2

3. The average value of the numbers 15, 21, 32, 35, 46, x, 59, 65, 72 should be greater than or equal to 43 but less than or equal to 44. Then the value of x should be
(1) 42 ≤ x ≤ 51
(2) 43 ≤ x ≤ 50
(3) 42 < x ≤ 49
(4) 43 < x < 50

Solution :1

4. The base of a right pyramid is an equilateral triangle of side 4 cm. The height of the pyramid is half of its slant height. Its volume is

Solution :3

5. Water flows in a tank 150 m x 100 m at the base, through a pipe whose cross-section is 2 dm by 1.5 dm, at the speed of 15 km per hour. In what time will the water be 3 metres deep ?
(1) 100 hours
(2) 120 hours
(3) 140 hours
(4) 150 hours

Solution :1

6. A tent is of the shape of a right circular cylinder upto a height of 3 metres and then becomes a right circular cone with maximum height of 13.5 metres above the ground. If the radius of the base is 14 metres, the cost of painting the inner side of the tent at the rate of Rs. 2 per square metre is
(1) Rs. 2,050
(2) Rs. 2,060
(3) Rs. 2,068
(4) Rs. 2,080

Solution :3

7. The sides of a triangle are 50 cm, 78 cm and 112 cm. The smallest altitude is
(1) 20 cm
(2) 30 cm
(3) 40 cm
(4) 50 cm

Solution :2

8. Rahim bought a gift item for Rs. 510 after getting a discount of 15%. He then sells it 5% – above the marked price. The profit earned in this deal is
(1) Rs. 150
(2) Rs. 120
(3) Rs. 100
(4) Rs. 90

Solution :2

9. The simple interest on a sum of money is 1/9 th of the principal and the number of years is equal to the rate percent per annum. The rate percent per annum is equal to

Solution :4

10. If x + y+ z 1, xy + yz + zx = -1, xyz = – 1, then x3 + y3 + z3 is
(1) -2
(2) -1
(3) 0
(4) 1

Solution :4

1. If x2 + y2 + z2 = xy + yz + zx, (x # 0), then the value of

Solution :3

Solution :3

3. The area of the triangle, formed by the graph of ax + by = c (where a, b are two positive real numbers) and the co-ordinate axes, is

Solution :3

4. A shopkeeper marks his goods at 40% above their cost price. He is able to sell 3/4 th of his goods at this price, and the remaining at 40% discount. Assuming that the shopkeeper is able to sell all the goods he buys, fmd his loss or gain as % on the whole transaction.

(1) 20% loss
(2) 23% loss
(3) 26% gain
(4) 30% gain

Solution :3

5. A fruit seller bought 240 bananas at the rate of Rs. 48 per dozen. He sells half of them at the rate of Rs. 5 per banana. 1/6 th of the remaining are found to be rotten. The price per banana at which he has to sell the remaining bananas to get a profit of 25% on his entire investment is
(1) Rs. 5.5
(2) Rs. 6.0
(3) Rs. 5.0
(4) Rs. 6.5

Solution :2

6. Two numbers are 30% and 40% more than the third number respectively. The first number is x% of the second. Then x =

Solution :4

7. The price of cooking oil has increased by 25%. The percentage of reduction that a family should effect in the use of cooking oil, so as not to increase the expenditure on this account, is
(1) 15%
(2) 20%
(3) 25%
(4) 30%

Solution :2

8. If a train runs at 40 km/hr, it reaches its destination late by 11 minutes, but if it runs at 50 km/ hr, it is late by 5 minutes only. Find, the correct time for the train to complete its journey.
(1) 19 minutes
(2) 20 minutes
(3) 21 minutes
(4) 18 minutes

Solution :1

9. If x = r cos θ cos Φ, y = r cos θ sin Φ and z = r sin θ, then the value of x2 + y2 + z2 is

Solution :1

10. If 5 cos θ + 12 sin θ = 13, tiler tan θ=

Solution :3

1. (1) 0
(2) 1
(3) 2
(4) 3

Solution :2

Solution :4

3. A man from the top of a 100 metre high tower sees a car moving towards the tower at an angle of depression of 30°. After some time, the angle of depression becomes 60°. The distance (in metres) travelled by the car during this time is

Solution :2

4. If the diameter of a sphere decreased by 25%, its curvets surface area will be decreased by
(1) 43.25%
(2) 43.50%
(3) 43.75%
(4) 44.25%

Solution :3

5. If x2 + y2 + z2 + 2 = 2(y – x), then value of x3 + y3 + z3 is equal to
(1) 0
(2) 1
(3) 2
(4) 3

Solution :1

6. O is the circumcentre of ABC. If ∠BAC = 85°, ∠BCA 75°, then ∠OAC is equal to
(1) 70°
(2) 60°
(3) 80°
(4) 100°

Solution :1

7. The distance between the centres of the two circles with radii 4 cm and 9 cm is 13 cm. The length of the direct common tangent (between two points of contact) is
(1) 13 cm
(2) √153 cm
(3) 12 cm
(4) 18 cm

Solution :3

8. The external bisector of ∠ABC of ΔABC intersects the straight line through A and parallel to BC at the point D. If ∠ABC = 50°, then measure of ∠ADB is
(1) 65°
(2) 55°
(3) 40°
(4) 20°

Solution :1

9. AB is a diameter of a circle with centre at 0. DC is a chord of it such that DC || AB. If ∠BAC = 20°, then ∠ADC is equal to
(1) 120°
(2) 110°
(3) 115°
(4) 100°

Solution :2

10. The tangents drawn at P and Q on the circumference of a circle intersect at A. If ∠PAQ = 68°, then the measure of the ∠APQ is
(1) 56°
(2) 68°
(3) 28°
(4) 34°

Solution :1

Directions ( 42 – 45) : Study the following table and answer the questions.
Number of students from various schools playing various games (one student plays one game only)

11. The difference between the total number of student:, saying Basketball from all the schools and the total number of students playing Cricket from all the schools is
(1) 27
(2) 35
(3) 28
(4) 26

Solution :2

12. The number of students playing Football from School C is x percent of the total number of students playing Football from all the schools. x equals

Solution :2

13. Which school has the maximum number of players ?
(1) A
(2) B
(3) C
(4) E

Solution :4

14. The number of students playing Badminton from School E is x% of the students playing Badminton from School B. Then x equals
(1) 40
(2) 50
(3) 42
(4) 41

Solution :2

Directions (46 – 50) : The following bar graph depicts the result for B.Sc. students of a college for three years. Read the graph and answer the questions based on this graph.

15. The number of students passed in 3rd division in 1984 was
(1) 165
(2) 75
(3) 70
(4) 65

Solution :3

16. The percentage of students failed in 1984 was

Solution :3

17. The aggregate pass percentage during the three years was

Solution :3

18. The percentage of students passed in 1st division in 1982 was