Math Ncert Exemplar 2019 Solutions for Class 7 Maths Chapter 4 - Simple Equations

Answer:

ax + b = 0
⇒ ax = –b
⇒ x = $\frac{-b}{a}$

Hence, the correct answer is option (c).
 

Answer:

a and b are positive integers.
∴ ax = b
⇒ $x=\frac{b}{a}$
Since, a, b > 0
 ⇒ $\frac{b}{a}>0$
$\therefore x=\frac{b}{a} \mathrm{is} \mathrm{always} \mathrm{positive}$

Hence, the correct answer is option (a).

Answer:

Dividing both sides of a equation by the same non-zero number is possible only.

Hence, the correct answer is option (d).

Answer:

(a) 2x + 6 = 0
⇒ 2x = –6
⇒ x = –3

(b) 3x – 5 = 0
⇒ 3x = 5
⇒ x = $\frac{5}{3}$

(c) 5x – 8 = x + 4
⇒ 5x – 8 = 4 + 8
⇒ 4x = 12
⇒ x = 3

(d) 4x + 7 = x + 2
⇒ 4x – x = 2 – 7
⇒ 3x = –5
⇒ x = $-\frac{5}{3}$
Thus, only $\frac{-5}{3}$ is neither a fraction nor an integer.

Hence, the correct answer is option (d).

 

Answer:

(a) 5y – 3 = –18
⇒ 5y = –18 + 3
⇒ y = $\frac{–15}{5}=–3$

(b) 3x – 9 = 0
⇒ 3x = 9
⇒ x = 3

(c) 3z + 8 = 3 + z
⇒ 3z – z = 3 – 8
⇒ 2z = –5
⇒ z = $\frac{-5}{2}$

(d) 9y + 8 = 4y – 7
⇒ 9y – 4y = –7 – 8
⇒ 5y = –15
⇒ y = –3
Thus, only z = $\frac{-5}{2}$ is not an integer.

Hence, the correct answer is option (c).
 

Answer:

7x + 4 = 25
⇒ 7x = 25 – 4
⇒ 7x = 21
⇒ x = 3

Hence, the correct answer is option (d).

Answer:

3x + 7 = –20
⇒ 3x = –20 – 7
⇒ 3x = –27
⇒  x = –9

Hence, the correct answer is option (b).

Answer:

y – 15 = 2y + 1
⇒ y – 2y = 1 + 15
⇒ –y = 16
⇒ y = –16

Hence, the correct answer is option (d).

Answer:

k + 7 = 16
⇒ k = 16 – 7
⇒ k = 9
∴ 8k – 72 = 8 × 9 – 72
= 72 – 72
= 0

​Hence, the correct answer is option (a).

Answer:

43m = 0.086
⇒ m = $\frac{0.086}{43}$
⇒ m = 0.002

Hence, the correct answer is option (a).

Answer:

x exceeds 3 can be represented as x = 3 + 7 
⇒ x – 3 = 7

Hence, the correct answer is option (c).

Answer:

(a) 4x + 1 = 2
⇒ 4x = 2 – 1 = 1
⇒ $x=\frac{1}{4}$

(b) 3 – x = 8 
⇒ –x = 8 – 3
⇒ –x = 5
⇒ x = –5

(c) x – 5 = 3
⇒ x = 5 + 3
⇒ x = 8

(d) 3 + x = 8
⇒ x = 8 – 3
⇒ x = 5
Thus, equation 3 + x = 8 has 5 as a solution.

Hence, the correct answer is option (d).
 

Answer:

(a) x + 3 = 1
⇒ x = 1 – 3
⇒ x = –2

(b) 8 + 2x = 3
⇒ 2x = –5
⇒ x = $\frac{-5}{2}$

(c) 10 + 3x =1
⇒ 3x = –9
⇒ x = –3

(d) 2x + 1 = 3
⇒ 2x = 2
⇒ x = 1
Thus, equation 10 + 3x = 1 has –3 as a solution.

Hence, the correct answer is option (c).
 

Answer:

(a) 2x + 1 = –1
⇒ 2x = –1 –1
⇒ x = –1

(b) $\frac{x}{2}+5=7$
$$\begin{gathered} \Rightarrow \frac{x}{2}=2 \\ \Rightarrow x=2\times 2=4 \end{gathered}$$

(c) 3x – 1 = –1
⇒ 3x = 0
⇒ x = 0

(d) 3x – 1 = 1
⇒ 3x = 2
⇒$x=\frac{2}{3}$
Thus, equation 3x – = –1 has 0 as a solution.

Hence, the correct answer is option (c). 
 

 

Answer:

(a) 2x + 1 = 15
⇒ 2x = 15 – 1 = 14
⇒ $x=\frac{14}{2}=7$

(b) 7x – 1 = 50
⇒ 7x = 50 + 1 = 51
⇒ x = $\frac{51}{7}$

(c) x – 3 = 4
⇒ x = 3 + 4 = 7

(d) $\frac{x}{7}-1=0$
$$\begin{gathered} \Rightarrow \frac{x}{7}=1 \\ \Rightarrow x=7\times 1=7 \end{gathered}$$

Thus, equation 7x – 1 = 50 can not be formed with x = 7.

Hence, the correct answer is option (b). 


 

Answer:

$\frac{x}{2}=3$
⇒ x = 3 × 2
⇒ x = 6
∴ 3x + 2 = 3 × 6 + 2
= 18 + 2
= 20

Hence, the correct answer is option (a).
 

Answer:

–6 + x = –12
⇒ x = –12 – (–6)
⇒ x = –12 + 6
⇒ x = –6

Hence, the correct answer is option (c).

Answer:

Shifting one term from one side of an equation to another side with a change of sign is known as transposition.

Hence, the correct answer is option (b).

Answer:

(a) 60 – x
(b) 60 – 2x
(c) 60 – 2x = 30
(d) 60 – 2x = 30
⇒ – 2x = 30 – 60
⇒ 2x = 30
⇒ x = 15
(e) 60 – x = 60 – 15 = 45
Numbers are 15 and 45.
 

Answer:

(a) 2x
(b) x + 2x = 81
⇒ 3x = 81
(c) We have,
3x = 81
⇒ x = 27
Thus, the solution of the equation is x = 27.
(d) The two numbers are x and 2x.
Here, x = 27
⇒ 2x = 2 × 27
= 54
​Thus, the two numbers are 27 and 54.
 

Answer:

(a) 2x
(b) 2(2x) + 3(x) = 280
⇒ 4x + 3x = 280
⇒ 7x = 280
(c) We have,
7x = 280
⇒ x = $\frac{280}{7}$ = 40
Thus, the solution of the equation is x = 40.
(d) Marks obtained by Abha are 80.

Answer:

(a) 2 × x = 2x cm
(b) Perimeter of rectangle = 2 × (length + breadth)
= 2 × (x + 2x)  
= 2 × 3x
= 6x
Thus, perimeter of rectangle in terms of x is 6x cm.
(c) The equation formed is 6x = 60.
(d) We have, 
6x = 60
⇒ x = 10
Thus, the solution of the equation is x = 10.
 

Answer:

(a) 5x
(b) 2x
(c) There are equal number of ₹5 and ₹2 coins in the bag. So,
5x + 2x = 70
⇒ 7x = 70
Thus, the equation formed is 7x = 70.
(d) We have, 
7x = 70
⇒ x = 10
Thus, there are 10 ₹5 coins and 10 ₹2 coins.

Hence, the correct answer is option (d).

Answer:

(a) 30 – x
(b) 2000x + 1000(30 – x)
(c) We have, 
2000x + 1000(30 – x) = 52000
⇒ 2000x + 30000 – 1000x = 52000
⇒ 1000x = 22000
(d) We have,
1000x = 2000
⇒ x = 22
​(e) Thus, the number of 1st prizes are 22 and the number of 2nd prizes are 8.

Answer:

We have,
z + 3 = 5
Subtracting 3 from both sides, (z + 3) – 3 = 5 – 3 
⇒ z = 2

Answer:

We have,
3x – 2 = 7
⇒ 3x = 7 + 2
⇒ 3x = 9
⇒ x = 3
Thus, x = 3 is the solution of equation 3x – 2 = 7.

Answer:

We have,
3x + 10 = 7
⇒ 3x = 7 – 10
⇒ 3x = –3
⇒ x = –1
Thus, x = –1 is the solution of 3x + 10 = 7.

Answer:

We have, 
2x + 3 = 5
⇒ 2x = 5 – 3
⇒ 2x = 2
⇒ x = 1
Now, 
3x + 2 = 3(1) + 2
= 3 + 2
= 5
Thus, the value of 3x + 2 is 5. 

Answer:

We have,
4x – 1 = 8
⇒ 4x = 8 + 1
⇒ 4x = 9
⇒ x = $\frac{9}{4}, \mathrm{which} \mathrm{is} \mathrm{not} \mathrm{an} \mathrm{integer}$
Thus. the equation 4x – 1 = 8 has no solution in integers.
 

Answer:

We have.
4x + 5 = –7
⇒ 4x = –7 – 5
⇒ 4x = –12
⇒ x = –3, which is not a natural number 
Thus, the equation 4x + 5 = –7 has no solution in natural numbers.

Answer:

We have.
x – 5 = –5
⇒ x = –5 + 5
⇒ x = 0, which is not a natural number 
Thus, the equation x – 5 = –5 has no solution in natural numbers.

Answer:

We have.
x + 8 = 12 – 4
⇒ x + 8 = 8
⇒ x = 8 – 8
⇒ x = 0, which is a whole number 
Thus, the equation x + 8 = 12 – 4 has one solution in natural numbers.

Answer:

Let the number be x.
When 5 is added to three times a number, it becomes (3x + 5)
When 7 is subtracted from four times of the number, it becomes (4x – 7).
Now,
3x + 5 = 4x – 7
This fact can be represented as 3x + 5 = 4x – 7.

Answer:

We have,
x + 7 = 10
⇒ x = 10 – 7
⇒ x = 3 
Thus, x + 7 = 10 has the solution x = 3.

Answer:

We have, 
3x = 12
⇒ x = 4
⇒ x – 0 = 4 – 0
⇒ x – 0 = 4
Thus, x – 0 = 4  when 3x = 12.

Answer:

We have,
2x = 2
⇒ x = 1
⇒ x – 1 = 1 – 1
⇒ x – 1 = 0
Thus, x – 1 = 0  when 2x = 2.

Answer:

$\frac{x}{2}=6$
⇒ x = 2 × 6
⇒ x = 12
Since, 12 + 3 = 15
⇒ 12 – (–3) = 15
⇒ x –  (–3)  = 15
 

Answer:

x + 15 = 19
⇒ x = 19 – 15
⇒ x = 4

Answer:

Finding the value of a variable in a linear equation that satisfies the equation is called a root of the equation.

Answer:

Any term of an equation may be transposed from one side of the equation to the other side of the equation by charging the sign of term.

Answer:

$$\begin{gathered} \frac{9}{5}x\mathit{ }= \frac{18}{5} \\ \Rightarrow \frac{9}{5}x÷\frac{9}{5}=\frac{18}{5}÷\frac{9}{5} \\ \Rightarrow x=\frac{18}{5}\times \frac{5}{9}=2 \end{gathered}$$

Answer:

3 – x = –4
⇒ –x = –4 – 3
⇒ –x = –7
⇒ x = 7
 

Answer:

$$\begin{gathered} x-\frac{1}{2}=\frac{-1}{2} \\ \Rightarrow x=\frac{-1}{2}+\frac{1}{2} \\ \Rightarrow x=0 \end{gathered}$$

Answer:

$$\begin{gathered} \frac{1}{6}-x=\frac{1}{6} \\ \Rightarrow -x=\frac{1}{6}-\frac{1}{6} \\ \Rightarrow -x=0 \\ \Rightarrow x=0 \end{gathered}$$

Answer:

Let the number be x.
∴ x – 10 = 65
⇒ x = 65 + 10
⇒ x = 75
Thus, the number is 75.

Answer:

Let the number be p.
∴ p + 20 = 45
⇒ p = 45 – 20
⇒ p = 25
Thus, the number is 25.
 

Answer:

Let the number is 25.
∴ 84 – x = 12
⇒ –x = 12 – 84
⇒ –x = –72
⇒ x = 72
Thus, the number is 72.

Answer:

$x-\frac{7}{8}=\frac{7}{8}$
⇒ $x=\frac{7}{8}+\frac{7}{8}$
⇒ $x=\frac{7+7}{8}$
⇒ $x=\frac{14}{8}$
⇒ $\frac{7}{4}$

Answer:

3x + 2 = 17
⇒ 3x = 17 – 2 = 15
⇒ $\frac{3x}{3}=\frac{15}{3}$
⇒ x = 5
Thus, 5 is the solution of 3x + 2 = 17.

Answer:

4x – 1 = 8
⇒ 4x = 8 + 1 = 9
⇒ $\frac{4x}{4}=\frac{9}{4}$
⇒ $\frac{9}{4}$
Thus, the statement is false.

Answer:

4x – 5 = 7
⇒ 4x = 7 + 5 = 12
⇒ $\frac{4x}{4}=\frac{12}{4}$
⇒ x = 3, is an integer
Thus, the statement is false.

Answer:

Let the number be x.
∴ One-third of the number = $\frac{x}{3}$
As per the question,
$\frac{x}{3}+x=10$
Thus, the statement is false.

Answer:

8x – 5 = 7
⇒ 8x = 7 + 5 = 12
⇒ $\frac{8x}{8}=\frac{12}{8}$
⇒ $x=\frac{3}{2}$
Thus, the statement is true.

Answer:

4x – 7 = 11
⇒ 4x = 11 + 7 = 18
⇒ $\frac{4x}{4}=\frac{18}{4}$
⇒ $x=\frac{9}{2}$
Thus, the statement is false.

Answer:

$$\begin{gathered} \frac{5x-7}{2}=y \\ \Rightarrow \frac{5\times 9–7}{2}=y \\ \Rightarrow y=\frac{45–7}{2} \\ \Rightarrow y=\frac{38}{2} \\ \Rightarrow y=19 \end{gathered}$$
Thus, the statement is false.

Answer:

(i) x + 5 = 9
⇒ x = 9 – 5
⇒ x = 4     (C)
(ii) x – 7 = 4
⇒ x = 7 + 4
⇒ x = 11   (E)
(iii) $\frac{x}{12}=–5$
⇒ x = I2 × (–5)
⇒ x = –60    (F)
(iv) 5x = 30
⇒ $\frac{5x}{5}=\frac{30}{5}$
⇒ x = 6    (D)
(v) 3y = 5
⇒ $\frac{3y}{3}=\frac{5}{3}$
⇒ $y=\frac{5}{3}$    (B)
(vi) $\frac{1}{3}\left(1-3p\right)=\frac{1}{3}\left(1-3\times 2\right)$
$$\begin{gathered} =\frac{1}{3}\left(1-6\right) \\ =\frac{1}{3}\times \left(-5\right) \\ =\frac{-5}{3} \left(\mathrm{A}\right) \end{gathered}$$










 

Answer:

Let the number be x.
∴ 2x – 13 = 3
Thus, the given statement can be written in equation as 2x – 13 = 3.

Answer:

Let the number be x.
So, one-fifth of the number = $\frac{x}{5}$x5
Therefore, $\frac{x}{5}=x-5$ is the required equation.

Answer:

Let the number be x.
So, one-third of number = $\frac{x}{3}$
7 more than $\frac{x}{3}=\frac{x}{3}+7$
Therefore, $x=\frac{x}{3}+7$ is the required equation

Answer:

Let the number be x.
So, six times of the number = 6x
Therefore, 6x – x + 10 is the required equation.

Answer:

Let the number be x.
So, half of the number $=\frac{x}{2}$ x2
On subtracting 10 from it, we get $\frac{x}{2}-10$x2−10
Therefore , $\frac{x}{2}-10=4$ is the required equation.

Answer:

The number is p.
On subtracting 5 from it, we get p – 5.
∴ p – 5 = 2 is the required equation.

Answer:

Let the number be x.
So, five times of the number = 5x
When increased by 7, it gives the expression 5x +7
∴ 5x + 7 = 27 is the required equation.

Answer:

Let Sohan is x years old.
So, Mohan is x + 3 years old.
∴ Sum of their ages be x + (x + 3).
∴ x + (x + 3) = 43 is the required equation.

Answer:

Let the number be x.
On subtracting 1 from it, we get x – 1.
Multiplying it by $\frac{1}{2}$ we get $\frac{1}{2}\left(x-1\right)$
∴ $\frac{1}{2}\left(x-1\right)=7$ is the required equation.

Answer:

Let the number be x.
Dividing the number by 2, we get $\frac{x}{2}$.
When, increased by 5, it gives the expression $\frac{x}{2}+5$
∴ $\frac{x}{2}+5=9$ is the required equation.

Answer:

Let the number be x.
So, twice of the number = 2x
On adding 4 to it, we get 2x + 4
∴ 2x + 4 = 18 is the required equation.

Answer:

Let the age of Amit be x years.
So, age of Sohan Lal = 4x years
According to question, 4x – x = 27
$$\begin{gathered} \Rightarrow 3x=27 \\ \Rightarrow x=9 \end{gathered}$$
Thus, Amit is 9 years old.

Answer:

Let the number be x.
∴ Other number = x +12
According to question,
x + x + 12 = 72
⇒ 2x + 12 = 72
⇒ 2x = 72 – 12 = 60
⇒ x = 30
∴ x + 12 = 30 + 12 = 42
Hence, the numbers are 30 and 42

Answer:

Let the number be x.
So, seven times of the number = 7x
Thirteen times of the number = 13x
According to question,
7x = 13x – 12
⇒ 12 = 13x – 7x
⇒ 6x = 12
⇒ x = 2⇒x=126=2
Thus, 2 is the required number.

Answer:

Let the interest received by Ramesh be x.
So, interest received by Karim = ₹ (30+ x)
According to question,
x + x + 30 = 70
⇒ 2x = 70 – 30 = 40
⇒ x = 20
Thus, ₹ 20 is the interest received by Ramesh.

Answer:

Let the amount of money donated by Subramaniam be x.
So, the amount paid by Naidu is (x + 125).
According to question,
x + x + 125 = 975
⇒ 2x = 975 – 125 = 850
⇒ x = 425
Thus, ₹425 is donated by Subramaniam.

Answer:

Let the number of girls be x.
So, the number of boys = x – 50
According to question,
x + x – 50 = 1070
⇒ 2x = 1070 + 50 = 1120
⇒ x = 560
Thus, 560 are girls.

Answer:

Let the number be x.
So, two times of the number = 2x
When, increased by 5, it gives the expression 2x + 5
∴ 2x + 5 = 9
⇒ 2x = 9 – 5 = 4
⇒ x = 2
Thus, x = 2 is the required number.

Answer:

Let the number be x.
So, twice of the number = 2x
On adding 9 to it, we get 2x + 9
∴ 2x + 9 = 13
⇒ 2x = 13 – 9 = 4
⇒ x = 2
Thus, x = 2 is the required number.

Answer:

Let the number be x.
So, one third of the number $\frac{x}{3}$.
On subtracting 1 from it, we get $\frac{x}{3}-1$x3−1
$$\begin{gathered} \frac{x}{3}-1=1 \\ \Rightarrow \frac{x}{3}=1+1=2 \\ \Rightarrow x=6 \end{gathered}$$
Thus, x = 6 is the required number.

Answer:

Let present age of Rama be x years.
So, five times of his age = 5x.
According to question,
5x = x + 25
⇒ 5x – x = 25
⇒ 4x = 25
⇒ x = $\frac{25}{4}$

Thus, at present Rama is $\frac{25}{4}$ years old.

Answer:

Let present age of Manoj be x years.
So, five times of his age = 5x
According to question,
5 = x + 20
⇒ 5x – x = 20
⇒ 4x = 20
⇒ x = 5
Thus, at present Manoj is 5 years old.

Answer:

Let present age of my younger sister be x years.
After 3 years, her age will be = (x + 3) years
Before 3 years, her age was = (x – 3) years
According to question,
x = 3 (x + 3) – 3 (x – 3)
⇒ x = 3 (x + 3 – x + 3)
⇒ x = 3(6) = 18
Thus, at present my younger sister is 18 years old.

Answer:

Let the number be x.
So, half of the number $\frac{x}{2}$.
On adding 45 to it, we get $\frac{x}{2}+45$.

$$\begin{gathered} \frac{x}{2}+45=3x \\ 3x-\frac{x}{2}=45 \\ \frac{6x-x}{2}=45 \\ \frac{5x}{2}=45 \\ x=18 \end{gathered}$$

Thus, the number is 18.

Answer:

Let the quantity of rice consumed in the family be x kg.
So, quantity of wheat consumed = 4x kg
According to question, x + 4x = 80
⇒ 5x = 80
⇒ x = 16

Thus, 16 kg rice consumed in the family and 4 × 16 = 64 kg wheat consumed in the family.

Answer:

Let two rupees coins are x in numbers.
So, one rupee coins are 3x in numbers.
According to question, 1(3x) + 2(x) = 120
⇒ 3x + 2x = 120
⇒ 5x = 120
⇒ x = 24
Thus, 3 × 24 = 72 coins are of one rupee coins.

Answer:

Let the number Anamika thought be x.
Multiplying it by 2, we get 2x
On adding 5 to it, we get 2x + 5
∴ 2x + 5 = 17
⇒ 2x = 17 – 5 = 12
⇒ x = 6
Thus, she had thought of number 6.

Answer:

Let the one number be x.
So, other number = 2x
According to question,
x + 2x = 12
⇒ 3x = 12
⇒ x = 4

∴ Other number is 2x = 2 × 4 = 8.

Answer:

Let the smallest integer be x
So, next two consecutive integer would be x + 1 and x + 2 respectively.
According to question,
x + x + 1 + x + 2 = x + 5
⇒ 3x + 3 = x + 5
⇒ 3x – x = 5 – 3
⇒ 2x = 2
⇒ x = 1
Thus, next two consecutive integers are 2 and 3 respectively.

Answer:

Let the number be x.
Dividing it by 6, we get $\frac{x}{6}$.
$$\begin{gathered} \frac{x}{6}=6 \\ x=6\times 6 \\ x=36 \end{gathered}$$
Thus, x = 36 is the required number.

Answer:

Let the breadth of rectangle be x m.
So, five times of breadth = 5x
Therefore, length of rectangle = (5x – 4) m
Perimeter of rectangle = 40 m
⇒ 2(x + 5x – 4) = 40
⇒ 2(6x – 4) = 40
⇒ 6x – 4 = 20
⇒ 6x = 20 + 4 = 24
⇒ x = 4
Thus, length of rectangle = (5 × 4 – 4) = 16 m

Answer:

Let length of equal sides of an isosceles triangle be 2x cm.
So, the third side of triangle x cm.
Perimeter of triangle = 30 cm
⇒ x + 2x + 2x = 30
⇒ 5x = 30
⇒ x = 6
Thus, 6 cm, 12 cm and 12 cm are the required sides of the triangle.

Answer:

Let first multiple of 2 be x.
So, next multiple of 2 = x + 2
According to question,
x + x + 2 = 18
⇒ 2x = 18 – 2 = 16
⇒ x = 8
Thus, 8 and 10 are required numbers.

Answer:

Let one angle be x.
So, complement of x = 90°– x
According to question,
x – (90°– x) = 20°
⇒ x – 90° + x = 20°
⇒ 2x = 20° + 90° = 110°
⇒ x = 55°
∴ Complement of x = 90°– x = 90°– 55° = 35°
Thus, 55° and 35° are required complementary angles.

Answer:

Let first part be x.
So, other part = 150 – x
According to question, 2x = 150 – x
⇒ 2x + x = 150
⇒ 3x = 150
⇒ x = 50

Thus, other part = 150 – x = 150 – 50 = 100
Hence, 150 has been divided into 50 and 100.

Answer:

Let the number of boys in class = x
So, the number of girls in class = 60 – x
According to question,
$60-x=\frac{x}{3}$
⇒ 180 – 3x = x
⇒ 180 = 3x + x
⇒ 4x = 180
⇒ x = 45
Thus, number of boys in the class = 45
And number of girls in the class = 60 – 45 = 15

Answer:

Let the number be x.
So, two-third of numbers $\frac{2}{3}x$.
According to question,
$$\begin{gathered} \frac{2}{3}x=\frac{1}{3}x+3 \\ \frac{2x}{3}-\frac{x}{3}=3 \\ \frac{2x-x}{3}=3 \\ \frac{x}{3}=3 \\ x=9 \end{gathered}$$
Thus, x = 9 is the required number.

Answer:

Let the number be x.
According to question,
x – 27 = 73 – x
⇒ x + x = 73 + 27
⇒ 2x = 100
⇒ x = 50

Thus, x = 50 is the required number.

Answer:

Let the length of total journey be x km.
∴ Journey by train = x km
∴ Joumey by bus = $\frac{2}{5}x km$
∴ Journey by car = $\frac{x}{3}$ km
And journey on foot = $\frac{x}{4}$ km
$$\begin{gathered} x=\frac{2x}{5}+\frac{x}{3}+\frac{x}{4}+3 \\ x=\frac{24x+20x+15x}{60}+3 \\ x=\frac{59x}{60}+3 \\ x-\frac{59x}{60}=3 \\ \frac{x}{60}=3 \\ x=3\times 60 \\ x=180 \end{gathered}$$

Thus, x = 180 km is the length of total journey.

Answer:

Let the number be x.
According to question,
$$\begin{gathered} 2x+\frac{x}{2}=24 \\ \frac{4x+x}{2}=24 \\ 5x=2\times 24=48 \\ x=\frac{48}{5} \\ x=9.6 \end{gathered}$$

Thus, x = 9.6 is the required number.

Answer:

Let the number be x.
So, thrice of the number = 3x
When it decreased by 5, we get 3x – 5
According to question,
3x – 5 = 2x + 1
⇒ 3x – 2x = 1 + 5
⇒ x = 6
Thus, x = 6 is the required number.

Answer:

Let the age of father be x years.
So, age of his girl = (x – 28) years
According to question,
x + x – 28 = 50
⇒ 2x = 50 + 28 = 78
⇒ x = 39
Thus, age of father = 39 years
And age of his girl = 11 years

Answer:

Let the width of rectangle be x cm.
So, the length of rectangle = 2x
Perimeter of rectangle = 180 cm
⇒ 2(2x + x) = 180
⇒ 6x = 180
⇒ x = 30
Thus, width of rectangle = 30 cm
And length of rectangle = 2 × 30 = 60 cm

Answer:

Let the cost of one pencil be ₹ x
So, the cost of 5 pencils = ₹ 5x
Cost of 7 pencils = ₹ 7x
According to question,
7x = 5x + 6
⇒ 7x – 5x = 6
⇒ 2x = 6
⇒ x = 3
Cost of 10 pencils = ₹ (3 × 10) = ₹ 30

Answer:

Let number of students got first division in 2006 be x.
So, the number of students got first division in 2007 = 3768 – x.
According to question,
3768 – x = x + 34
⇒ 3768 – 34 = x + x
⇒ 2x = 3734
⇒ x = 1867
Thus, 1867 students got first division in 2006.

Answer:

Let Radha’s monthly salary = ₹ x
So, money got by her in over time = ₹ (17480 – x)
According to question,
x = 17480 – x + 10000
⇒ x + x = 17480 + 10000
⇒ 2x = 27480
⇒ x = 13740
Thus, ₹13740 is her monthly salary.

Answer:

Since, square has all sides equal
∴ 18x – 20 = 42 – 13x
⇒ 18x + 13x = 42 + 20
⇒ 31x = 62
⇒ x = 2
∴ Side of square = 18 × 2 – 20 = 36 – 20 = 16
Thus, length of the side of the square is 16 units.

Answer:

(a) Incorrect equation is


After removing two matchsticks the correct equation is
GRAPHIC

(b) Incorrect equation is
GRAPHIC

After removing one matchstick the correct equation is
GRAPHIC

Answer:

i + 69 = 70
⇒ i = 70 – 69 = 1

8u = 6u +8
⇒ 8u – 6u = 8
⇒ 2u = 8
⇒ u = 4

4a = –5a + 45
⇒ 4a + 5a = 45
⇒ 9a – 45
⇒ a = 5

4q + 5 = 17
⇒ 4q = 17 – 5
⇒ 4q = 12
⇒ q = 3

–5t – 60 = – 70
⇒ –5t = –70 + 60
⇒ –5t = –10
⇒ t = 2

$$\begin{gathered} \frac{1}{4}s+98=100 \\ \frac{1}{4}s=2 \\ s=8 \\ \frac{5}{3}p+9=24 \\ \frac{5}{3}p=15 \\ p=9 \\ 3c=c+12 \\ 3c-c=12 \\ 2c=12 \\ c=6 \\ 3(k+1)=24 \\ k+1=8 \\ k=7 \end{gathered}$$

Thus, 1 = i, 2 = t, 3 = q, 4 = u, 5 = a, 6 = c, 7 = k, 8 = s, 9 = p.

Answer:

Given that • = 3.

$$\begin{gathered} \left(a\right) 5*=2∆=2• \\ \left(b\right) 2∆=2*+2• \\ \left(c\right) 3*+3•=3∆ \end{gathered}$$
Solving equations, we get
$$\begin{gathered} 5*=2*+2•+2• \\ 5*-2*=4• \\ 3*=4\times 3 \\ *=4 \end{gathered}$$
$\begin{array}{rcl}3∆& =& 3\times 4+3\times 3\\ & =& 12+9\\ & =& 21\\ ∆& =& 7\end{array}$

Answer: