linear equations Model Questions & Answers, Practice Test for ssc cgl tier 1 2023

Answer: (a)

Let the total no of boys be n.

Now, No of boys above 160 cm height = 18

$3/4$ n = 18

n = 24

Also, let total no of students be N.

Then, n = $2/3$ N = 36

n = $3/2$ (24) = 36

∴ Number of girls = N – n = 36 – 24 = 12

Answer: (c)

Given equations are

5x – 2y = 10

2x + 6y = 21

On solving, we get

x = 3 and y = 5/2

Their interaction point is (3, 5/2) The shaded region shows the graph below the original region.

So solution set is

5x – 2y ≤ 10 and 2x + 6y ≤ 21

∴ Option (c) is correct.

Answer: (d)

Suppose number of passengers be x in the starting. Number of passengers after $1^{st}$ halt

= $(x - x/3) + 120 = {2x}/3$ + 120

Number of passengers after 2nd halt

= $1/2({2x}/3 + 120)$ + 100

According to question,

Number of passengers after $2^{nd}$ halt

= $1/2 ({2x}/3 + 120)$ + 100 = 240

⇒${2x}/3$ + 120 = (240 – 100) × 2

⇒${2x}/3$ = 280 – 120

${2x}/3$ = 160

x = ${160 × 3}/2 = {80 × 3}/1$

x = 240

Answer: (d)

Let Pooja's initial salary is Rs.x and fixed increment every year is Rs.y.

According to question,

x + 3y = 4200 ... (i)

and x + 8y = 6800 ... (ii)

On solving equations (i) and (ii), we get

x = Rs.2640, y = Rs.520

Answer: (b)

Given system of equations are:

x + 2y = 3 and 3x + 6y = 9

⇒x + 2y = 3

Here, ${a_1}/{a_2} = {b_1}/{b_2} = {c_1}/{c_2} = 1/3$

So, it has infinitely many solutions.