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Aptitude Algebraic Expressions Test Paper 3


11) In an institution, half of the students went on industrial tour. 12 times of the square root of total students went to see the industrial fair and remaining 128 students were allotted a project work. Total number of students in the institution is

  1. 576
  2. 288
  3. 1024
  4. None of above

Answer: C

Explanation:

Let the numbers of students be x
Then
Apti Algebraic Expressions12Apti Algebraic Expressions= 128
x-24Apti Algebraic Expressions= 256
x-24Apti Algebraic Expressions-256 = 0
Let Apti Algebraic Expressions =y

Then,

y2 - 24y-256=0

y2 - (32-8)y-256=0

y(y-32)+8(y-32)=0

(y+8)(y-32)=0

y = - 8,y=32

∴ x=y2= 322=1024


12) Two mixers and one T.V. cost Rs. 7000 while two T.V.'s and 'one mixer cost Rs. 8,800. What is the price of one mixer (in Rupees)?

  1. 1400
  2. 1300
  3. 1250
  4. 1100

Answer: A

Explanation:

Let the price of mixer is Rs. x

And, the price of a T.V = Rs y.

As per the question:

2x + y = 7,000........(i)

x + 2y = 9,800 ........(ii)

x = 9800 - 2y

2(9800 - 2y) + y = 7000

19600 - 4y + y = 7000

19600 - 3y = 7000

19600 - 7000 = 3y

12600 = 3y

y= 12600/3 = 4200

Putting the value of y in equation (ii)

x + 2 * 4200 = 9800

x = 9800 - 8400

x = 1400


13) The solution of the equations
Apti Algebraic Expressions is.

  1. x=4,y=3
  2. x=4,y=-3
  3. x=-4,y=-3
  4. x=-4,y=3

Answer: B

Explanation:

Apti Algebraic Expressions= 2,

=>Apti Algebraic Expressions = 2

=> 5x + 4y = 8

Also,

Apti Algebraic Expressions= 2

=>Apti Algebraic Expressions = 2

4x + 3y = -5

Solving these equations, we get

x = 4, y = - 3


14) The cost of 3 kg potatoes and 2 kg tomatoes is Rs. 32 and that of 1 kg potato and 4 kg tomatoes of the same type is Rs. 39. The cost (in Rupees) of potatoes and tomatoes per kg are respectively

  1. 5 and 17
  2. 18 and 5
  3. 5 and 17/2
  4. 3 and 17/2

Answer: C

Explanation:

Let the cost of potatoes per kg = Rs. X

And the cost of tomatoes per kg = Rs. Y

3x + 2y = 32 ........ (i)

x + 4y = 39 ........ (ii)

Solving equation 1 and 2, we get
x = 5,y = Apti Algebraic Expressions


15) Today Madan is 20 years younger than his father. Ten years ago he was one-half as old as his father. How old his father is ten years hence?

  1. 40 years
  2. 50 years
  3. 60 years
  4. Data inadequate

Answer: C

Explanation:

Let the age of Madan and his father be x and y years respectively. Then

y-x = 20 .........(i)

Ten year ago:
x-10=Apti Algebraic Expressions (y-10)

2(x-10) = y - 10

2x - 20 = y - 10

2x - y = - 10 + 20

2x - y = 10

Now solving eq.1 and eq.2:

y - x = 20

- y + 2x = 10

x = 30 (age of Madan)

So, age of his father: y = x + 20

                        = 30 + 20 = 50

Madan's father age after 10 years:

y+10 = 50 + 10 = 60 years


Aptitude Algebraic Expressions Test Paper 1
Aptitude Algebraic Expressions Test Paper 2
Aptitude Algebraic Expressions Test Paper 4





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