Basic Equations - Online Quiz



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Following quiz provides Multiple Choice Questions (MCQs) related to Basic Equations. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz.

Questions and Answers

Q 1 - On solving 2x+y=8 and 3y=4+4x, we get:

A - x=3, y=-4

B - x=2, y=4

C - x=1, y=4

D - x=4, y=1

Answer : B

Explanation

The given equations are
2x+ y=8...  (1)     4x-3y=-4 ...(2)
On multiplying (1) by 3 and adding (2) to it, we get:
 10x= 20
 ⇒x= 2
Putting x= 2 in (1), we get: 4+ y = 8   ⇒y = 4
∴ x= 2, y= 4

Q 2 - If 2x+3y = 29 and y = x+3, what is the estimation of x?

A - 4

B - 5

C - 6

D - none of these

Answer : A

Explanation

Putting y = x+3 in 2x+3y = 29, we get :
2x+3 (x+3) = 29 ⇒5x = 20
 ⇒x= 4

Q 3 - If 3x+7y= 75 and 5x-5y= 25, then what is the estimation of x+y?

A - 14

B - 15

C - 16

D - 17

Answer : D

Explanation

Given 3x+7y = 75  ...(i)
5x-5 y= 25 ⇒x-y = 5...(ii)
Multiplying (ii) by 7 and adding to (i), we get:
10 x = 110   ⇒x = 11
Putting x = 11 in (ii), we get: y=(11-5) = 6
∴ x+y = (11+6) = 17

Answer : B

Explanation

Given equations are p/x+q/y = m...(i),   q/x+ p/y = n ...(ii)
On multiplying (i) by q, (ii) by p and subtracting, we get:
q2/y- p2/y = mq-np
⇒y (mp-np) = (q2- p2)
⇒y = (q2-p2)/(mq- np)
= (p2- q2)/(np-mq)
On multiplying (i) by p, (ii) by q and subtracting, we get:
p2/x - q2/x = mp- nq
⇒ (p2- q2) = x (mp- nq)
⇒x = (p2- q2)/ (mp-nq)
∴ x= (p2-q2)/(mp-nq) , y = (p2-q2)/(np- mq)

Q 5 - The arrangement of 3x-y+1/3 = 2x+y+2/5 = 3x+2y+1/6 are given by:

A - x=1, y=2

B - x=-1, y=-1

C - x=1, y=1

D - x=2 , y=1

Answer : C

Explanation

We have (3x-y+1)/3= (2x+y+2)/5
⇒5 (3x-y+1) =3(2x+y+2)
⇒15x-5y+5 = 6x+3y+6
⇒9x-8y -1 = 0 ⇒9x-8y = 1 ...(i)
And (2x+y+2)/5 = (3x+2y+1)/6
⇒ 6 (2x+y+2) = 5(3x+2y+1)
⇒12x+6y +12=   15x+10 y+5
⇒3x+ 4y= 7...(ii)
Multiplying (ii) by 2 and adding (i) to it, we get: 15x= 15 ⇒x= 1
Putting x =1 in .., (ii), we get 3*1+4y= 7 ⇒4y = 4 ⇒y = 1
∴ x= 1, y = 1

Q 6 - On the off chance that 4x+6y =32 and 4x-2y= 4, then 8y =?

A - 24

B - 30

C - 36

D - none of these

Answer : D

Explanation

4x+6y = 32...(i) 4x-2y = 4...(ii)
On subtracting (ii) from (i), we get: 8 y= 28

Q 7 - The arrangement of 2x+3y=2 and 3x+2y =2 can be spoken to by a point in the direction plane in:

A - First quadrant

B - second quadrant

C - third quadrant

D - fourth quadrant

Answer : A

Explanation

2x+3y = 2...(i) , 3x+2y= 2...(ii)
Multiplying (i) by 2 and (ii) by 3 and subtracting, we get: -5x= -2 ⇒x= 2/5
Putting x= 2/5 in (i), we get 4/5+3y= 2 ⇒3y = (2-4/5) = 6/5 ⇒y = 6/5*1/3 =2/5
∴ the solution can be represented by a point (2/5, 2/5) which lies in 1st quadrant.

Q 8 - The arrangement of mathematical statements 2x+ℏy= 11 and 5x-7y = 5 have no arrangement when:

A - ℏ= 13/5

B - ℏ=-13/5

C - ℏ=-14/5

D - ℏ=-16/5

Answer : C

Explanation

For no solution , we have a₁/a₂ = b₁/b₂ ≠c₁/c₂
i.e. 2/5 = ℏ/-7 ≠11/5 ⇒ℏ= -14/5 

Answer : B

Explanation

Here a₁/a₂= 1/2, b₁/b₂=2/4=1/2 and c₁/c₂=3/3=1.
∴ a₁/a₂=b₁/b₂≠c₁/c₂.
∴Give system has no solution.

Q 10 - In the event that 3 seats and 1 table expense Rs. 900 and 5 seats and 3 tables cost Rs. 2100, then the expense of 4 seats and 1 table is:

A - Rs. 1000

B - Rs. 1050

C - Rs. 1100

D - Rs. 1150

Answer : B

Explanation

Let cost of 1 chair =Rs x and cost of 1 table =Rs y. Then,
3x+y=900   ...(i)             5x+3y=2100      ...(ii)
On multiplying (i) by 3 and subtracting (ii) from it, we get: 4x=600⇒x=150.
Putting x=150 in (i), we get: 3*150+y=900⇒y= (900-450) =450.
Cost of (4 chairs+1 table) =Rs (4*150+1*450) =Rs (600+450) =Rs1050.


aptitude_basic_equations.htm

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