Rs Aggarwal 2019 2020 Solutions for Class 8 Math Chapter 8 Linear Equations are provided here with simple step-by-step explanations. These solutions for Linear Equations are extremely popular among Class 8 students for Math Linear Equations Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2019 2020 Book of Class 8 Math Chapter 8 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2019 2020 Solutions. All Rs Aggarwal 2019 2020 Solutions for class Class 8 Math are prepared by experts and are 100% accurate.

Solve:
8x + 3 = 27 + 2x

Solve:
5x + 7 = 2x − 8

Solve:
2z − 1 = 14 − z

#### Question 4:

Solve:
9x + 5 = 4(x − 2) + 8

#### Question 5:

Solve:
$\frac{7y}{5}=y-4$

#### Question 6:

Solve:
$3x+\frac{2}{3}=2x+1$

#### Question 7:

Solve:
15(y − 4) − 2(y − 9) + 5(y + 6) = 0

#### Question 8:

Solve:
3(5x − 7) − 2(9x − 11) = 4(8x − 13) − 17

#### Question 9:

Solve:
$\frac{x-5}{2}-\frac{x-3}{5}=\frac{1}{2}$

#### Question 10:

Solve:
$\frac{3t-2}{4}-\frac{2t+3}{3}=\frac{2}{3}-t$

#### Question 11:

Solve:
$\frac{2x+7}{5}-\frac{3x+11}{2}=\frac{2x+8}{3}-5$

#### Question 12:

Solve:
$\frac{5x-4}{6}=4x+1-\frac{3x+10}{2}$

#### Question 13:

Solve:
$5x-\frac{1}{3}\left(x+1\right)=6\left(x+\frac{1}{30}\right)$

#### Question 14:

Solve:
$4-\frac{2\left(z-4}{3}=\frac{1}{2}\left(2z+5\right)$

#### Question 15:

Solve:
$\frac{3\left(y-5\right)}{4}-4y=3-\frac{\left(y-3\right)}{2}$

#### Question 16:

Solve:
$\frac{8x-3}{3x}=2$

#### Question 17:

Solve:
$\frac{9x}{7-6x}=15$

#### Question 18:

Solve:
$\frac{3x}{5x+2}=-4$

#### Question 19:

Solve:
$\frac{6y-5}{2y}=\frac{7}{9}$

#### Question 20:

Solve:
$\frac{2-9z}{17-4z}=\frac{4}{5}$

#### Question 21:

Solve:
$\frac{4x+7}{9-3x}=\frac{1}{4}$

#### Question 22:

Solve:
$\frac{7y+4}{y+2}=\frac{-4}{3}$

#### Question 23:

Solve:
$\frac{15\left(2-y\right)-5\left(y+6\right)}{1-3y}=10$

#### Question 24:

Solve:
$\frac{2x-\left(7-5x\right)}{9x-\left(3+4x\right)}=\frac{7}{6}$

#### Question 25:

Solve:
$m-\frac{\left(m-1\right)}{2}=1-\frac{\left(m-2\right)}{3}$

#### Question 26:

Solve:
$\frac{3x+5}{4x+2}=\frac{3x+4}{4x+7}$

#### Question 27:

Solve:
$\frac{9x-7}{3x+5}=\frac{3x-4}{x+6}$

#### Question 28:

Solve:
$\frac{2-7x}{1-5x}=\frac{3+7x}{4+5x}$

#### Question 1:

Two numbers are in the ratio 8 : 3. If the sum of the numbers is 143, find the numbers.

#### Question 2:

$\frac{2}{3}$ of a number is 20 less than the original number. Find the number.

#### Question 3:

Four-fifths of a number is 10 more than two-thirds of the number. Find the number.

#### Question 4:

Twenty-four is divided into two parts such that 7 times the first part added to 5 times the second part makes 146. Find each part.

#### Question 5:

Find the number whose fifth part increased by 5 is equal to its fourth part diminished by 5.

#### Question 6:

Three numbers are in the ratio of 4 : 5 : 6. If the sum of the largest and the smallest equals the sum of the third and 55, find the numbers.

#### Question 7:

If 10 be added to four times a certain number, the result is 5 less than five times the number. Find the number.

#### Question 8:

Two numbers are such that the ratio between them is 3 : 5. If each is increased by 10, the ratio between the new numbers so formed is 5 : 7. Find the original numbers.

#### Answer:

Let us consider x as the common multiple of both the number.
Then, first number = 3x
Second number = 5x

Therefore, the common multiple of both the numbers is 5.
First number =
Second number =

#### Question 9:

Find three consecutive odd numbers whose sum is 147.

#### Question 10:

Find three consecutive even numbers whose sum is 234.

#### Question 11:

The sum of the digits of a two-digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54, find the original number. Check your solution.

#### Question 12:

The digit in the tens place of a two-digit number is three times that in the units place. If the digits are reversed, the new number will be 36 less than the original number. Find the original number. Check your solution.

#### Question 13:

The denominator of a rational number is greater than its numerator by 7. If the numerator is increased by 17 and the denominator decreased by 6, the new number becomes 2. Find the original number.

#### Question 14:

In a fraction, twice the numerator is 2 more than the denominator. If 3 is added to the numerator and to the denominator, the new fraction is $\frac{2}{3}$. Find the original fraction.

#### Question 15:

The length of a rectangle exceeds its breadth by 7 cm. If the length is decreased by 4 cm and the breadth is increased by 3 cm, the area of the new rectangle is the same as the area of the original rectangle. Find the length and the breadth of the original rectangle.

#### Question 16:

The width of a rectangle is two-thirds its length. If the perimeter is 180 metres, find the dimensions of the rectangle.

#### Question 17:

An altitude of a triangle is five-thirds thelength of its corresponding base. If the altitude be increased by 4 cm and the base decreased by 2 cm, the area of the triangle remains the same. Find the base and the altitude of the triangle.

#### Question 18:

Two angles of a triangle are in the ratio 4 : 5. If the sum of these angles is equal to the third angle, find the angles of the triangle.

#### Question 19:

A steamer goes downstream from one port to another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of the stream be 1 km/h, find the speed of the steamer in still water and the distance between the ports.

#### Question 20:

The distance between two stations is 300 km. Two motorcyclists start simultaneously from these stations and move towards each other. The speed of one of them is 7 km/h more than that of the other. If the distance between them after 2 hours of their start is 34 km, find the speed of each motorcyclist. Check your solution.

#### Question 21:

Divide 150 into three parts such that the second number is five-sixths the first and the third number is four-fifths the second.

#### Question 22:

Divide 4500 into two parts such that 5% of the first part is equal to 10% of the second part.

#### Question 23:

Rakhi's mother is four times as old as Rakhi. After 5 years, her mother will be three times as old as she will be then. Find their present ages.

#### Question 24:

Monu's father is 26 years younger than Monu's grandfather and 29 years older than Monu. The sum of the ages of all the three is 135 years. What is the age of each one of them?

#### Question 25:

A man is 10 times older than his grandson. He is also 54 years older than him. Find their present ages.

#### Question 26:

The difference between the ages of two cousins is 10 years. 15 years ago, if the elder one was twice as old as the younger one, find their present ages.

#### Question 27:

Half of a herd of deer are grazing in the field and three-fourths of the remaining are playing nearby. The rest 9 are drinking water from the pond. Find thenumber of deer in the herd.

#### Question 1:

Tick (✓) the correct answer:
If 2x − 3 = x + 2, then x = ?
(a) 1
(b) 3
(c) 5
(d) 7

(c) 5

#### Question 2:

Tick (✓) the correct answer:
If $5x+\frac{7}{1}=\frac{3}{2}x-14,$ then x = ?
(a) 5
(b) −5
(c) 6
(d) −6

#### Question 3:

Tick (✓) the correct answer:
If
(a) 40
(b) 20
(c) 10
(d) 60

(a) 40

#### Question 4:

Tick (✓) the correct answer:
If 3m = 5m$-\frac{8}{5}$, then m = ?
(a) $\frac{2}{5}$
(b) $\frac{3}{5}$
(c) $\frac{4}{5}$
(d) $\frac{1}{5}$

#### Answer:

(c) $\frac{4}{5}$

#### Question 5:

Tick (✓) the correct answer:
If 5t − 3 = 3t − 5, then t = ?
(a) 1
(b) −1
(c) 2
(d) −2

(b) -1

#### Question 6:

Tick (✓) the correct answer:
If $2y+\frac{5}{3}=\frac{26}{3}-y$, then y = ?
(a) 1
(b) $\frac{2}{3}$
(c) $\frac{6}{5}$
(d) $\frac{7}{3}$

#### Answer:

(d) $\frac{7}{3}$

#### Question 7:

Tick (✓) the correct answer:
If $\frac{6x+1}{3}+1=\frac{x-3}{6}$, then x = ?
(a) 1
(b) −1
(c) 3
(d) −3

(b) -1

#### Question 8:

Tick (✓) the correct answer:
If $\frac{n}{2}-\frac{3n}{4}+\frac{5n}{6}=21,$ then n = ?
(a) 30
(b) 42
(c) 36
(d) 28

(c) 36

#### Question 9:

Tick (✓) the correct answer:
If $\frac{x+1}{2x+3}=\frac{3}{8}$, then x = ?
(a) $\frac{1}{4}$
(b) $\frac{1}{3}$
(c) $\frac{1}{6}$
(d) $\frac{1}{2}$

#### Answer:

(d) $\frac{1}{2}$

#### Question 10:

Tick (✓) the correct answer:
If $\frac{4x+8}{5x+8}=\frac{5}{6},$ then x = ?
(a) 4
(b) 6
(c) 8
(d) 12

(c) 8

#### Question 11:

Tick (✓) the correct answer:
If $\frac{n}{n+15}=\frac{4}{9}$, then n = ?
(a) 4
(b) 6
(c) 9
(d) 12

(d) 12

#### Question 12:

Tick (✓) the correct answer:
If 3(t − 3) = 5(2t + 1), then t = ?
(a) −2
(b) 2
(c) −3
(d) 3

(a) -2

#### Question 13:

Tick (✓) the correct answer:
Four-fifths of a number is greater than three-fourths of the number by 4. The number is
(a) 12
(b) 64
(c) 80
(d) 102

(c) 80

#### Question 14:

Tick (✓) the correct answer:
The ages of A and B are in the ratio 5 : 7. Four years from now the ratio of their ages will be 3 : 4. The present age of B is
(a) 20 years
(b) 28 years
(c) 15 years
(d) 21 years

(b) 28 years

#### Question 15:

Tick (✓) the correct answer:
The base of an isosceles triangle is 6 cm and its perimeter is 16 cm. Length of each of the equal sides is
(a) 4 cm
(b) 5 cm
(c) 3 cm
(d) 6 cm

(b) 5 cm

#### Question 16:

Tick (✓) the correct answer:
Sum of three consecutive integers is 51. The middle one is
(a) 14
(b) 15
(c) 16
(d) 17

(d) 17

#### Question 17:

Tick (✓) the correct answer:
The sum of two numbers is 95. If one exceeds the other by 15, then the smaller of the two is
(a) 40
(b) 35
(c) 45
(d) 55

(a) 40

#### Question 18:

Tick (✓) the correct answer:
Number of boys and girls in a class are in the ratio 7 : 5. The number of boys is 8 more than the number of girls. The total class strength is
(a) 56
(b) 52
(c) 48
(d) 36

(c) 48

#### Question 1:

Subtract 4a2 + 5b2 − 6c2 + 8 from 2a2 − 3b2 − 4c2 − 5.

#### Question 2:

Find each of the following products:
(i) (4a + 5b) × (5a − 6b)
(ii) (6x2 − x + 8) × (x2 − 3)

#### Question 3:

Divide (5a3 − 4a2 + 3a + 18) by (a2 − 2a + 3).

#### Answer: Therefore, is the quotient.

#### Question 4:

If $\left(x-\frac{1}{x}\right)=4$, find the value of
(i) $\left({x}^{2}+\frac{1}{{x}^{2}}\right).$
(ii) $\left({x}^{4}+\frac{1}{{x}^{4}}\right).$

#### Answer:

2 + 2  42 + 2  16 + 2  18

#### Question 5:

Evaluate {(83)2 − (17)2}.

#### Question 6:

Factorise:
(i) x3 − 3x2 + x − 3
(ii) 63x2y2 − 7
(iii) 1 − 6x + 9x2
(iv) 7x2 − 19x − 6

#### Question 7:

Solve: $\frac{2x+7}{3x+5}=\frac{15}{17}.$

#### Question 8:

5 years ago a man was 7 times as old as his son. After 5 years he will be thrice as old as his son. Find their present ages.

#### Question 9:

Mark (✓) against the correct answer:
ab
ab + 1 = ?
(a) (1 − a)(1 − b)
(b) (1 − a)(b − 1)
(c) (a − 1)(b − 1)
(d) (a − 1)(1 − b)

#### Answer:

(c) (a-1)(b-1)

$ab-a-b+1\phantom{\rule{0ex}{0ex}}=a\left(b-1\right)-1\left(b-1\right)\phantom{\rule{0ex}{0ex}}=\left(a-1\right)\left(b-1\right)$

#### Question 10:

Mark (✓) against the correct answer:
3 + 23x − 8x2 = ?
(a) (1 − 8x)(3 + x)
(b) (1 + 8x)(3 − x)
(c) (1 − 8x)(3 − x)
(d) none of these

(b)

#### Question 11:

Mark (✓) against the correct answer:
7x2 − 19x − 6 = ?
(a) (x − 3)(7x + 2)
(b) (x + 3)(7x − 2)
(c) (x − 3)(7x − 2)
(d) (7x − 3)(x + 2)

#### Answer:

(a)

$7{x}^{2}-19x-6\phantom{\rule{0ex}{0ex}}=7{x}^{2}-21x+2x-6\phantom{\rule{0ex}{0ex}}=7x\left(x-3\right)+2\left(x-3\right)\phantom{\rule{0ex}{0ex}}=\left(x-3\right)\left(7x+2\right)$

#### Question 12:

Mark (✓) against the correct answer:
12x2 + 60x + 75 = ?
(a) (2x + 5)(6x + 5)
(b) (3x + 5)2
(c) 3(2x + 5)2
(d) none of these

(c)

#### Question 13:

Mark (✓) against the correct answer:
10p2 + 11p + 3 = ?
(a) (2p + 3)(5p + 1)
(b) (5p + 3)(2p + 1)
(c) (5p − 3)(2p − 1)
(d) none of these

#### Answer:

(b)

$10{p}^{2}+11p+3\phantom{\rule{0ex}{0ex}}=10{p}^{2}+5p+6p+3\phantom{\rule{0ex}{0ex}}=5p\left(2p+1\right)+3\left(2p+1\right)\phantom{\rule{0ex}{0ex}}=\left(5p+3\right)\left(2p+1\right)$

#### Question 14:

Mark (✓) against the correct answer:
8x3 − 2x = ?
(a) (4x − 1)(2x − 1)x
(b) (2x2 + 1)(2x − 1)
(c) 2x(2x − 1)(2x + 1)
(d) none of these

(c)

#### Question 15:

Mark (✓) against the correct answer:

(a) x = 3
(b) x = 4
(c) x = 5
(d) x = 2

(b)

#### Question 16:

Fill in the blanks.
(i) x2 − 18x + 81 = (......)
(ii) 4 − 36x2 = (......)(......)(......)
(iii) x2 − 14x + 13 = (......)(......)
(iv) 9z2x2 − 4y2 + 4xy = (......)(......)
(v) abcabc + 1 = (......)(......)

#### Answer:

(i)

(ii) $\left(4\right)\left(1-3x\right)\left(1+3x\right)$

(iii) $\left(x-13\right)\left(x-1\right)$

(iv) $\left(3z+x-2y\right)\left(3z-x+2y\right)$

(v) $\left(c-1\right)\left(ab-1\right)$

#### Question 17:

Write 'T' for true and 'F' for false for each of the following:
(i) (5 − 3x2) is a binomial.
(ii) −8 is a monomial.
(iii) (5a − 9b) − (−6a + 2b) = (−a − 7b).
(iv) When x = 2 and y = 1, the value of
(v) $\frac{x}{4}+\frac{x}{6}-\frac{x}{2}=\frac{3}{4}⇒x=-9.$
(vi) $2x-5=0⇒x=\frac{2}{5}.$

#### Answer:

(i) T
Binomial expression is an expression that shows the sum or the difference of two unlike terms. The above expression has two unlike terms, i.e. 5 and 3x2.

(ii) T
Any expression that contains only one term is called a monomial. It can either be a constant or a variable.

(iii) F

(iv) T

(v) T

(vi) F

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