# 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

Explanation:

Let the numbers of students be x
Then 12 = 128
x-24 = 256
x-24 -256 = 0
Let =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

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 is.

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

Explanation: = 2,

=> = 2

=> 5x + 4y = 8

Also, = 2

=> = 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

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 = 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

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= (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

### Feedback   