Linear Equations Model Questions Set 1 Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (b)

Let the two-digit number be 10y + x.

According to question,

x + y = 10 ... (i)

and 10y + x – 18 = 10x + y

⇒9x – 9y = –18

⇒x – y = –2 ... (ii)

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

x = 4 and y = 6

∴ Required product = xy = 4 × 6 = 24.

Answer: (c)

Let there be (x + 1) members. Then,

Father's share = $1/4$ , share of each other member = $3/{4x}$.

∴ 3 $(3/{4x}) = 1/4$⇔4x = 36⇔x=9

Hence, total number of family member = 10.

Answer: (c)

Given that,

2x – 3y = 5 ... (i)

and –4x + 6y = 11 ... (ii)

Also, ${a_1}/{a_2} = 2/{-4} = {-1}/2$

${b_1}/{b_2} = {-3}/6 = {-1}/2$

⇒${a_1}/{a_2} ={b_1}/{b_2} = {-1}/2 ≠ {c_1}/{c_2}$

So, both equations are in parallel. So, it is not solved graphically.

Hence, A and R are individually true and R is correct explanation of A.

Answer: (a)

Let the positive number be x.

According to the question,

x + 10 = ${200}/x$

⇒ $x^2$ + 10x = 200

⇒ $x^2$ + 10x – 200 = 0

⇒ (x – 10) (x + 20) = 0

∴ x = 10, –20

But x ≠ –20, since x is a positive number

The required number is 10.

Answer: (d)

∴ x = ${135}/5$ = 27

Answer: (a)

Let x be the first digit and y be the second digit of two digit number.

According to question,

x + y = 8 ... (i)

(10x + y) – (10y + x) = 18

⇒9x – 9y = 18

⇒x – y = 2 ... (ii)

Adding (i) and (ii),

x + y = 8

x - y = 2

We get

2x = 10

⇒ x = 5

⇒ y = 8 – 5 = 3

⇒ x = 5 and y = 3

∴ Required difference of digits, x – y

= 5 – 3 = 2.