AP State Syllabus AP Board 8th Class Maths Solutions Chapter 2 Linear Equations in One Variable Ex 2.4 Textbook Questions and Answers.

## AP State Syllabus 8th Class Maths Solutions 2nd Lesson Linear Equations in One Variable Exercise 2.4

Question 1.

Find the value of ’x’ so that l || m

Solution:

Given l|| m. Then 3x – 10° = 2x + 15°

[Vertically opposite angles and corresponding angles are equal.]

⇒ 3x – 10 = 2x + 15

⇒ 3x – 2x = 15 + 10

∴ x = 25°

Question 2.

Eight times of a number reduced by 10 is equal to the sum of six times the number and 4. Find the number.

Solution:

Let the number be ‘x’ say.

8 times of a number = 8 × x = 8x

¡f10 is reduced from 8x then 8x – O

6 times of a number = 6 × x = 6x

If 4 is added to 6x then 6x + 4

According to the sum,

8x – 10 = 6x + 4

⇒ 8x – 6x = 4 + 10

⇒ 2x = 14

⇒ x = 7

∴ The required number = 7

Question 3.

A number consists of two digits whose sum is 9. If 27 is subtracted from the number its digits are reversed. Find the number.

Solution:

Let a digit of two digit number be x.

The sum of two digits = 9

∴ Another digit = 9 – x

The number = 10 (9 – x) + x

= 90 – 10x + x

= 90 – 9x

If 27 is subtraçted from the number its digits are reversed.

∴ (90 – 9x) – 27 = 10x + (9 – x)

63 – 9x = 9x + 9

9x + 9x = 63 – 9

18x = 54

∴ x = \(\frac { 54 }{ 18 }\) = 3

∴ Units digit = 3

Tens digit = 9 – 3 = 6

∴ The number = 63

Question 4.

A number is divided into two parts such that one part is 10 more than the other. If the two parts are in the ratio 5:3, find the number and the two parts.

Solution:

If a number is divided into two parts in he ratio of 5 : 3, let the parts be 5x, 3x say.

According to the sum,

5x = 3x + 10

⇒ 5x – 3x = 10

⇒ 2x = 10

∴ x = \(\frac { 10 }{ 2 }\)

∴ x = 5

∴ The required number be

x + 3x = 8x

= 8 × 5 = 40

And the parts of number are

5 = 5 × 5 = 25

3 = 3 × 5 = 15

Question 5.

When I triple a certain number and add 2, I get the same answer as I do when I subtract the number from 50. Find the number.

Solution:

Let the number be x’ say.

3 times of a number = 3 × x = 3x

If 2 is added to 3x then 3x + 2

If ‘xis subtracted from 50 then it becomes 50 – x.

According to the sum,

3x + 2 = 50 – x

3x + x = 50 – 2

4x = 48 .

x = 12

∴ The required number 12

Question 6.

Mary is twice older than her sister. In 5 years time, she will be 2 years older than her sister. Find how old are they both now.

Solution:

Let the age of Marys sister = x say.

Mary’s age = 2 × x = 2x

After 5 years her sister’s age

= (x + 5) years

After 5 years Mary’s age

= (2x + 5) years

According to the sum,

2x + 5 = (x + 5) + 2

= 2x – x = 5 + 2 – 5

∴ The age of Mary’s sister = x = 2 years

Mary’s age = 2x = 2 x 2 = 4 years

Question 7.

In 5 years time, Reshma will be three times old as she was 9 years ago. How old is she now?

Solution:

Reshma’s present age = ‘x’ years say.

After 5 years Reshmats age

= (x + 5) years

Before 9 years Reshma’s age

=(x – 9) years

According to the sum

= x+ 5 = 3(x – 9) = 3x – 27

x – 3x = -27-5

-2x = -32

x = \(\frac{-32}{-2}\) = 16

∴ x = 16

∴ Reshma’s present age = 16 years.

Question 8.

A town’s population increased by 1200 people, and then this new population decreased 11%. The town now had 32 less people than it did before the 1200 increase. Find the original population.

Solution:

Let th population of a town after the increase of 1200 is x say.

11% of present population

The present population of town

= 11,200 – 1200 = 10,000

Question 9.

A man on his way to dinner shortly after 6.00 p.m. observes that the hands of his watch form an angle of 110°. Returning before 7.00 p.m. he notices that again the hands of his watch form an angle of 1100. Find the number of minutes that he has been away.

Solution:

Let the number be ‘x ray.

\(\frac { 1 }{ 3 }\) rd of a number = \(\frac { 1 }{ 3 }\) x x = \(\frac { x }{ 3 }\)

\(\frac { 1 }{ 5 }\) th of a number = \(\frac { 1 }{ 5 }\) x x = \(\frac { x }{ 5 }\)

According to the sum

∴ x = 30

∴ The required number is 30.