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

Answer: (b)

Let the cost of one book = Rs.x

and the cost of one pencil = Rs.y

According to question,

4x + 3y = 8x + y

⇒2y = 4x⇒y = 2x

∴ Cost of 4 books and 3 pencils

= 4x + 3y = 4x + 6x = 10x

Cost of 6 books and 2 pencils

= 6x + 2y = 6x + 4x = 10x

Answer: (a)

Let,

fare from P→Q = Rs.x

fare from P→R = Rs.y

According to question,

x + y = Rs.42 ... (i)

5x + 10y = Rs.350 ... (ii)

By solving equations (i) and (ii), then we get

x = 14

y = 28

∴ fare from station P→R = Rs.14

Answer: (a)

Let the numerator = x and denominator = y

According to question,

$x/{y + 1} = 1/2$

⇒2x = y + 1

⇒2x – y = 1 ... (i)

and ${x + 1}/y$ = 1 ⇒ x + 1 = y

⇒ x – y = –1 ... (ii)

2x – y = 1

⇒${- x ± y = ± 1}/{x = 2}$

Putting the value of x in equation (ii),

2 – y = –1

⇒ y = 3⇒x = 2 and y = 3

∴ Required fraction = $x/y = 2/3$ .

Answer: (a)

Let smaller number = x

Larger number = 80 – x

According to question,

80 – x = 4x + 5

⇒5x = 75⇒x = 15

Answer: (d)

${2x - 3y + 1}/2 = {x + 4y + 8}/3 = {4x - 7y + 2}/5$

= ${(2x - 3y + 1) + (x + 4y + 8) - (4x - 7y + 2)}/{(2 + 3) - 5}$

= –x + 8y + 7 = x – 8y = 7

⇒x = 7 + 8y ... (i)

Now taking first two terms,

3(2x – 3y + 1) = 2(x + 4y + 8)

4x – 17y = 13

Putting the value of x from equation (i), then we get

4(7 + 8y) – 17y = 13

28 + 32y – 17y = 13

15y = –15

y = –1

Now putting the value of y in equation (i), then we get

x = 7 – 8 = –1

Then, x + y = –1 – 1 = –2

Hence, x + y = –2.