linear equations Model Questions & Answers, Practice Test for ibps clerk prelims 2023

Answer: (c)

Let the unit digit of the number be x and tens digit be y.

∴ Number = 10y + x

According to the question,

x + y = 10 ... (i)

and 10x + y = (10y + x) – 36

⇒10x + y – 10y – x = –36

⇒9x – 9y = –36

⇒x – y = –4 ... (ii)

⇒x = 3

From equation (i),

3 + y = 10

⇒y = 7

⇒x = 3 and y = 7

∴ Required product of two digits = 3 × 7 = 21

Answer: (b)

Let the two digit number be 10x + y.

According to the question, 10x + y = 3 (x + y)

⇒ 10x + y – 3x – 3y = 0

⇒ 7x – 2y = 0 ... (i)

According to question

⇒ (10x + y) + 45 = 10y + x

⇒ 10x + y + 45 – 10y – x = 0

⇒ 9x – 9y + 45 = 0

⇒ x – y = – 5 ... (ii)

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

x = 2 and y = 7

digit = 10 × 2 + 7 = 27

∴ sum of the squares of digits = $(2)^2 + (7)^2$

= 4 + 49 = 53

Answer: (c)

10x + y – 10y – x = 9

⇒9(x – y) = 9⇒x – y = 1

Answer: (e)

7x – 5y = 20 ...(i)

12x + 5y = 75 ...(ii)

Adding both the equations,

19x = 95 or, x = ${95}/{19}$ = 5

From equation (i),

7 × 5 – 5y = 20 or, 5y = 35 – 20

or, y = ${15}/5$ = 3 ∴ xy = 5 × 3 = 15

Answer: (a)

2x + y = x + 2y

x = y

Now, ${x^2}/{y^2} = {x^2}/{x^2}$ = 1