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

Answer: (a)

Let full fare = Rs.x and reservation charges = Rs.y

∴ x + y = 362 ... (i)

and 1$1/2$ x + 2y = 554

⇒3x + 4y = 1108 ... (ii)

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

∴ x = 340 and y = 22

Reservation charge = Rs.22

Answer: (b)

a + b = 2c

⇒ a + b = c + c

⇒ a – c = c – b ⇒ b - c = -(a - c)

$a/{a - c} + c/{b - c} = a/{a - c} + c/{-(a - c)}$

= $a/{a - c} - c/{a - c} = {a - c}/{a - c}$ = 1

Answer: (c)

Let the cost of chair be x and the cost of table be y, then

2x + y = 700 ... (i)

and x + 2y = 800 ... (ii)

From equations (i) and (ii), we get

⇒ y = 300

∴ x = 800 – 600 = 200

Given the number of chairs and tables are m to be purchased for Rs. 30000

According to question,

∴ 200m + 300m = 30000

m = ${30000}/{500}$ ⇒ m = 60

Answer: (b)

$7(x + 2a)^2 + 3a^2$ = 5a (7x + 23a)

⇒7$(x^2 + 4a^2 + 4ax) + 3a^2 = 35ax + 115a^2$

⇒ $x^2 – ax – 12a^2$ = 0

⇒ (x + 3a) (x – 4a) = 0

⇒ x = – 3a and x = 4a

m and n are the roots of the given equation.

Let m = 4a and n = –3a

Now, 3m – n = 3(4a) – (–3a) = 12a + 3a = 15a

Answer: (e)

Let the number of parrots be p and the number of tigers be t.

Then

p + t = 858 ...(i)

2p + 4t = 1846 ...(ii)

After rearranging equation (ii), we get

p + 2t = 923 ...(iii)

Solving (i) & (ii), we get

t = 65 & p = 793