MCQ: Linear Equations - 2 - SSC CGL MCQ

# MCQ: Linear Equations - 2 - SSC CGL MCQ

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## 15 Questions MCQ Test Quantitative Aptitude for SSC CGL - MCQ: Linear Equations - 2

MCQ: Linear Equations - 2 for SSC CGL 2024 is part of Quantitative Aptitude for SSC CGL preparation. The MCQ: Linear Equations - 2 questions and answers have been prepared according to the SSC CGL exam syllabus.The MCQ: Linear Equations - 2 MCQs are made for SSC CGL 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MCQ: Linear Equations - 2 below.
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MCQ: Linear Equations - 2 - Question 1

### The linear equation such that each point on its graph has an ordinate four times its abscissa is :

Detailed Solution for MCQ: Linear Equations - 2 - Question 1

Let us assume the abscissa coordinate be x and Ordinate be y.
According to question,
ordinate four times its abscissa
y = 4x
⇒ y - 4x = 0

MCQ: Linear Equations - 2 - Question 2

### Joel purchased 40 notebooks at the rate of Rs.18 per notebook and 55 pencils at the rate of Rs. 8 per pencil. What is the total amount that he paid to the shopkeeper?

Detailed Solution for MCQ: Linear Equations - 2 - Question 2

According to question,
40 notebooks at the rate of Rs. 18 per notebook and 55 pencils at the rate of Rs. 8 per pencil.
Amount paid = Rs. (40 x 18 + 55 x 8)
Amount paid = Rs. (720 + 440)
Amount paid = Rs. 1160

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MCQ: Linear Equations - 2 - Question 3

### If the numerator of a fraction is increased by 200% and the denominator is increased by 200% then resultant fraction is 14/5.What is the original fraction ?

Detailed Solution for MCQ: Linear Equations - 2 - Question 3

Let us assume the original fraction be x/y.
According to question,
200x/100 / 200y/100 = 14/5
2x/2y = 14/5
⇒x/y = 14/5

MCQ: Linear Equations - 2 - Question 4

A number of two digits has 3 for its unit's digit, and the sum of digits is 1/7 of the number itself, The number is

Detailed Solution for MCQ: Linear Equations - 2 - Question 4

Let the ten's digit be x. Then, number = 10x + 3 and sum of digits = ( x + 3 )
So ,(x+3) = 1/7(10x + 3)
⇔ 7x + 21 = 10x + 3
⇔ 3x = 18
⇔ x=6
Hence, the number = 10x + 3 = (10 x 6) + 3 = 63.

MCQ: Linear Equations - 2 - Question 5

The ratio of two numbers is 4:7. If each of those numbers increased by 30, their ratio will become 5:8 . What is the average of these two numbers ?

Detailed Solution for MCQ: Linear Equations - 2 - Question 5

Let the numbers be x and y.
According to question,
The ratio of two numbers is 4:7.
⇒ x/y = 4/7
⇒ 7x = 4y
∴ 7x - 4y = 0 ........................(1)
Again According to question,
If each of those numbers increased by 30, their ratio will become 5:8
(x + 30) / (y + 30) = 5/8
⇒ 8(x + 30) = 5(y + 30)
⇒ 8x + 240 = 5y + 150
⇒ 8x - 5y = -90 ..........................(2)
Multiply 5 with equation (1) , we will get.
35x - 20y = 0 ..................(3)
Multiply 4 with equation (2), we will get.
32x - 20y = -360 ............(4)
Subtracts the Equation (4) from Equation (3). we will get,
35x - 20y - (32x - 20y) = 0 - (-360)
⇒ 35x - 20y - 32x + 20y = 360
⇒ 3x = 360
⇒ x = 120
Put the value of x in equation (1) to get the value of y.
7x - 4y = 0
⇒ 7(120) - 4y = 0
⇒ 840 - 4y = 0
⇒ 4y = 840
⇒ y = 210
∴ Average of the numbers = (x + y)/2
put the vale of x and y.
∴ Average of the numbers = (120 + 210)/2
∴ Average of the numbers = 330/2
∴ Average of the numbers = 165

MCQ: Linear Equations - 2 - Question 6

Ravi has spent a quarter (1/4) of his life as a boy , one fifth (1/5) as a youth , one third (1/3) as a man and thirteen (13) years in old age . What is his present age ?

Detailed Solution for MCQ: Linear Equations - 2 - Question 6

Suppose that the Ravi present age is A years.
According to the given question,
A/4 + A/5 + A/3 + 13 = A
⇒ (15A + 12A + 20A)/60 = A - 13
⇒ 47A = 60A - 780
⇒60A - 47A = 780
⇒13A = 780
∴ A = 780/13 = 60 years

MCQ: Linear Equations - 2 - Question 7

The number obtained by interchanging the two digits of a two-digit number is lesser than the original number by 54. If the sum of the two-digit number is 10, then what is the original number ?

Detailed Solution for MCQ: Linear Equations - 2 - Question 7

Let us assume the digits of the original number are unit's digit a and ten's digit b.
The Original Number will be 10a + b.
After interchanging the digits the new number will be 10b + a.
According to question,
The number obtained by interchanging the two digits of a two-digit number is lesser than the original number by 54.
New Number = Original Number - 54
10b + a = 10a + b - 54
⇒ 10b + a - 10a - b = -54
⇒ 9b - 9a = -54
⇒ a - b = 6....................................(1)
Again according to question,
Sum of the digits of original number = 10
a + b = 10..................................................(2)
Add the equation (1) and (2), we will get
a - b + a + b = 10 + 6
2a = 16
a = 8
Put the value of a in Equation (2) , we will get
8 + b = 10
b = 10 - 8
b = 2
Put the value of a and b for original number, we will get
10a + b = 10 x 8 + 2 = 80 + 2 = 82

MCQ: Linear Equations - 2 - Question 8

The age of the father 5 years ago was 5 times the age of his son. At present the father's age is 3 times that of his son . What is the present age of the father ?

Detailed Solution for MCQ: Linear Equations - 2 - Question 8

Let us assume the present age of father = F year and Son's present age = S years
According to question, 5 years ago,
Father's age = F - 5 and Son's age = S - 5.
According to the question,
The age of the father 5 years ago was 5 times the age of his son.
F - 5 = 5(S - 5)
F - 5 = 5S - 25.....................(1)
At present the father's age is 3 times that of his son.
F = 3S.................................(2)
Put the value of F from equation (2) in equation (1), we will get
⇒ 3S - 5 = 5S - 25
⇒ 25 - 5 = 5S - 3S
⇒ 20 = 2S
⇒ 10 = S
⇒ S = 10.
Put the value of S in Equation (2). we will get,
F = 3S = 3 x 10 = 30
So the present Age of Father = 30.

MCQ: Linear Equations - 2 - Question 9

The sum of third , fourth and fifth part of a number exceeds half of the number by 34. Find the number?

Detailed Solution for MCQ: Linear Equations - 2 - Question 9

Let us assume N be the given number.
According to the question,
Sum of third , fourth and fifth part of a number exceeds half of the number by 34.
N/3 + N/4 + N/5 - 34 = N/2
N/3 + N/4 + N/5 - N/2 = 34
(20N + 15N + 12N - 30N)/60 = 34
17N/60 = 34
N = 34 x 60/17
N = 2 x 60
N = 120

MCQ: Linear Equations - 2 - Question 10

The value of k for which kx + 3y - k + 3 = 0 and 12x + ky = k, have infinite solutions, is

Detailed Solution for MCQ: Linear Equations - 2 - Question 10

For infinite solution
a1/a2 = b1/2 = c1/c2
⇒ K/12 = 3/K = (-K + 3)/ -K
⇒ K/12 = 3/K
⇒ K2 = 36
∴ K = √36 = 6

MCQ: Linear Equations - 2 - Question 11

If (x/4) + (y/3) = 10/24 and (x/2) + y = 1, then the value of x + y is

Detailed Solution for MCQ: Linear Equations - 2 - Question 11

Given, (x/4) + (y/3) = 10/24
⇒ (3x + 4y)/12 = 10/24
∴ 3x + 4y = 5 ...(i)
and (x/2) + y = 1
x + 2y = 2 ...(ii)
On multiplying Eq. (ii) by 2 and subtracting from Eq. (i).
3x + 4y = 5
2x + 4y = 4
- - -
--------------------------
x = 1
On putting the value of x in Eq. (ii), we get
x + 2y = 2
⇒ 1 + 2y = 2
⇒ y = 1/2

∴ x + y = 1 + 1/2 = 3/2

MCQ: Linear Equations - 2 - Question 12

The sum of the two digits is 15 and the difference between them is 3. What is the product of the digits ?

Detailed Solution for MCQ: Linear Equations - 2 - Question 12

Let the number be x and y.
Then, according to the question,
x + y = 15 ...(1)
x - y = 3 ...(ii)
on adding Eqs. (i) and (ii), we get
2x = 18
⇒ x = 9
On putting the value of in Eq. (i), we get
y = 6
∴ Product = xy = 54

MCQ: Linear Equations - 2 - Question 13
The numerator of a fraction is 6x + 1 and the denominator is 7 - 4x, x can have any value between -2 and 2, both included. The values of x for which the numerator is greater
Detailed Solution for MCQ: Linear Equations - 2 - Question 13

6x + 1 > 7 - 4x
⇒ x > 3/5
∴ 3/5 < x ≤ 2

MCQ: Linear Equations - 2 - Question 14

Deepak has some hens and some goats. If the total number of animal heads is 90 and the total number of animal feet is 248, what is the total number of goats Deepak has ?

Detailed Solution for MCQ: Linear Equations - 2 - Question 14

Let hens = H, goats = G
According to the question,
H + G = 90 ...(i)
2H + 4G = 248 ...(ii)
On multiplying Eq. (i) by 2 and subtracting from Eq. (ii) , we get
2H + 2G = 180
2H + 4G = 248
-------------------
-2G = -68
∴ G = 34

MCQ: Linear Equations - 2 - Question 15

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

Detailed Solution for MCQ: Linear Equations - 2 - Question 15

3x + 7y = 75 ..(i)
5x - 5y = 25
∴ x - y = 5 ...(ii)
On multiplying Eq. (ii) by 7 and adding to Eq. (i), we get
3x + 7y = 75
7x - 7y = 35
------------------
10x = 110
x = 11
∴ Putting the value of x in Eq. (ii), we get
11 - y = 5
∴ y = 6
∴ x + y = 6 + 11 = 17

## Quantitative Aptitude for SSC CGL

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## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests