# Exercise 2.4

Question 1:

Amina thinks a number and subtracts ​$$\dfrac{5}{2}$$​ from it . She multiplies the result by 8. The result now obtained is 3 times the same number she thought of . What is the number ?

Sol :

Let the number be x .

According to the given question,

$$8\Bigg(x-\dfrac{5}{2}\Bigg)=3x$$

5x = 20

Dividing both sides by 5 , we obtain

x = 4

Hence, the number is 4

Question 2:

A positive number is 5 times another number. If 21 is added to both the numbers , then one of the numbers becomes twice the other number. What are the numbers ?

Sol :

Let the numbers be x and 5x . According to the question,

21 + 5x = 2(x + 21)

21 + 5x = 2x +42

On transposing 2x to L.H.S and 21 to R.H.S , we obtain

5x – 2x = 42 – 21

3x = 21

Dividing both sides by 3, we obtain

x = 7

5x = ​$$5 \times{7}=35$$​

Hence , the numbers are 7 and 35 respectively

Question 3:

Sum of the digits of a two digit number is 9. When we interchange the digits it is found that the resulting new number is greater than the original number by 2. What is the two digit number ?

Sol :

Let the digits at tens place and once place be x and 9 – x respectively.

Therefore , original number = 10x + (9 – x) = 9x + 9

On interchanging the digits, the digits at ones place and tens place will be x and 9 – x respectively.

Therefore , new number after interchanging the digits = 10(9 – x) + x

= 90 – 10x + x

= 90 – 9x

According to the given question,

New number = Original number + 27

90 – 9x = 9x +9 +27

90 – 9x = 9x + 36

On transposing 9x to R.H.S and 36 to L.H.S , we obtain

90 – 36 = 18x

54 = 18x

Dividing both sides by 18 , we obtain

3 = x and 9 – x = 6

Hence, the digits at tens place and ones place of the number are 3 and  6 respectively.

Therefore, the two digit number is

= 9x + 9

= ​$$9\times{3}+9= 36$$​

Question 4:

One of the two digits of a two digit number is three times the other digit. If you interchange the digits of this two digit number and the resulting number to the original number, you get 88. What is the original number ?

Sol :

Let the digits at tens place and once place be x and 3x respectively.

Therefore , original number = 10x + 3x = 13x

On interchanging the digits, the digits at ones place and tens place will be x and 3x respectively.

Therefore , new number after interchanging the digits

\begin{align*}&=10\times3x+x\\&=30x+x\\&=31x\end{align*}

According to the given question,

New number + Original number = 88

13x + 31x = 88

44x = 88

Dividing both sides by 44 , we obtain

x = 2

Therefore,the original number ​\begin{align*}&=13x\\&=13\times2\\&=26\end{align*}

By considering the tens place and ones place as 3x and x respectively, the two digit number obtained is 62

Therefore , the two digit number may be 26 or 62

Question 5:

Shobo’s mother’s present age is six times Shobo’s present age. Shobo’s age five years from now will be one third of his mother’s present age. What are their present ages ?

Sol :

Let Shobo’s age be x years. Therefore, his mother’s age will be 6x years.

According to the given question,

After 5 years Shobo’s age ​$$=\dfrac{Shobo’s~mother’s~present~age}{3}$$

$$x+5=\dfrac{6x}{3}$$

x + 5 = 2x

On transposing x to R.H.S , we obtain

5 = 2x – x

5 = x

6x = ​$$6\times5=30$$

Therefore, the present ages of Shobo and Shobo’s mother will be 5 years and 30 years respectively.

Question 6:

There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11 : 4 . At the rate ₹ 100 per metre it will cost the village panchayat ₹ 75,000 to fence the plot. What are the dimensions of the plot ?

Sol :

Let the common ratio between the length and breadth of the rectangular plot be x . Hence , the length and breadth of the rectangular plot will be 11x m and 14x m respectively.

Perimeter of the plot

\begin{align*}&=2(l+b)\\&=2(11x +4x)m\\&=30x~m\end{align*}

It is given that the cost of fencing the plot at the rate of ₹ 100 per meter is ₹ 75,000

\begin{align*}100\times30x&=75000\\3000x&=75000\end{align*}

Dividing both sides by 3000, we obtain

x = 25

Length ​\begin{align*}&=11x~m\\&=(11\times25)m\\&=275m\end{align*}

Breadth ​\begin{align*}&=4x~m\\&=(4\times25)m\\&=100~m\end{align*}

Hence, the dimensions of the plot are 275 m and 100 m respectively.

Question 7:

Hasan buys two kinds of cloth materials for school uniforms, shirt material that cost him ₹ 50 per meter and trouser material that costs him ₹ 90 per meter. For every 2 meters of the trouser material he buys 3 meters of the shirt material. He sells the materials at 12% and 10% profit respectively. His total sale is ₹ 36660. How much trouser material did he buy ?

Sol :

Let 2x m of trouser material and 3x m of shirt material be bought by him.

Per meter selling price of trouser material

$$=₹~\Bigg(90+\dfrac{90\times12}{100}\Bigg)\\₹~100.80$$

Per meter selling price of shirt material

$$=₹~\Bigg(50+\dfrac{50\times10}{100}\Bigg)\\₹~55$$

Given that, the total amount of selling = ₹ 36660

\begin{align*}100.80\times(2x)+55\times(3x)&=36660\\201.60x+165x&=36660\end{align*}

366.60x = 36660

Dividing both sides by 366.60, we obtain

x = 100

Trouser material =2x m

$$=(2\times100)m\\=200~m$$

Question 8:

Half of a heard 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 the number of deer in the heard.

Sol :

Let the number of deer be x.

Number of deer grazing in the field = ​$$\dfrac{x}{2}$$

\begin{align*}{Number~of~deer~plaing~nearby}~&=\dfrac{3}{4}\times{Number~of~remaining~deer}\\&=\dfrac{3}{4}\times\bigg(x-\dfrac{x}{2}\bigg)\\&=\dfrac{3}{4}\times\dfrac{x}{2}\\&=\dfrac{3x}{8}\end{align*}

​Number of deer drinking water from the pond = 9

$$x-\bigg(\dfrac{x}{2}+\dfrac{3x}{8}\bigg)=9$$

$$x-\bigg(\dfrac{4x+3x}{8}\bigg)=9$$

$$x-\dfrac{7x}{8}=9$$

$$\dfrac{x}{8}=9$$

Multiplying both sides by 8, we obtain

x = 72

Hence, the total number of deer in the herd is 72

Question 9:

A grand father is ten times older than his granddaughter. He is also 54 years older than her. Find their present ages.

Sol :

Let the granddaughter’s age be x years. Therefore , granddaughter’ s age will be 10x years.

According to the question,

Grandfather’s age = Granddaughter’s age +54 years

10x – x = 54

9x = 54

x = 6

Granddaughter’s age = x years = 6 years

Grandfather’s age = 10x years

=  ​$$10\times6~years=60~years$$

Question 10:

Aman’s age is three times his son’s age. Ten years ago he was five times his son’s age. Find their present ages.

Sol :

Let Aman’s son’s age be x years. Therefore, Aman’s age will be 3x years. Ten years ago, their age was (x – 10) years and (3x – 10) years respectively.

10 years ago, Aman’s age = 5 times Aman’s son’s age 10 yeasr ago

3x 10 = 5(x – 10)

3x – 10 = 5x – 50

On transposing 3x to R.H.S and 50 to L.H.S, we obtain

50 – 10 = 5x – 3x

40 = 2x

Dividing both sides by 2 , we obtain

20 = x

Aman’s son’s age = x years = 20 years

Aman’s age = 3x years ​$$=3\times20=60~years$$

### 1 thought on “NCERT Solutions for class 8 Maths chapter 2 Linear Equation In One Variable”

1. Prestamos Con Pocos Intereses Con Dinero Prestamos Prestamo Privado Simulador De Prestamos Personales Credito Directo
Prestamos De Dinero Rapido Y Facil Prestamos Express Por Internet Prestamos Seguros Por Internet Prestamos Requisitos
Solicitar Credito Rapido Online Como Saber El Credito En Personal Creditos A Pagar A Plazos Solicitar Prestamo En Linea
Credito Familiar Pedir Credito Online Cuenta Prestamos

2. Donde Prestan Dinero Urgente Solo Credito Prestamos Cortos Y Rapidos Credito Dineo Prestamo Simple
https://prestamosurgente.space/denton-tx/
Prestamos Rapidos Nuevos Credito Rapid Credito Requisitos
https://prestamosurgente.space/egg-harbor-nj/
Hago Prestamos De Dinero Requisitos Para Solicitar Un Prestamo Personal Credito A 30 Dias Prestamos De Dinero En Linea Urgentes Te Presto Dinero Rapido
https://prestamosurgente.space/murrieta-ca/
Simulador Credito Nomina Lugares Donde Prestan Dinero Como Calcular El Interes De Un Prestamo Personal

3. Lugares De Prestamos De Dinero Banco Que Dan Prestamos Rapidos Prestamos Para Autonomos Prestamistas De Dinero Credito Directo
https://prestamosurgente.space/franklin-nj/
Empresas De Prestamos De Dinero Rapido Para Pedir Un Prestamo Prestamos Avance Pedir Dinero Online
https://prestamosurgente.space/frisco-tx/
Mini Prestamos Rapidos Online Financieras Prestamos Rapidos Solicitar Dinero Rapido Y Facil Credito Particular
https://prestamosurgente.space/phoenix-az/
Requisitos Para Pedir Un Prestamo Personal Hacer Un Prestamo Personal Requisitos Para Un Credito Personal El Dinero Rapido Prestamos A Plazos

4. Prestamos Baratos Mini Creditos Personales Consultar Credito Personal
https://creditosrapidosenusa.space/carson-city-nv/
Para Pedir Un Credito Rapido Solicitar Prestamo Personal Por Internet Creditos Y Prestamos Personales Como Conseguir Un Prestamo Facil
https://creditosrapidosenusa.space/savannah-ga/
Prestamos Por Linea Inmediatos Prestamistas Particulares Prestamo 300 Prestamos A Largo Plazo
https://creditosrapidosenusa.space/clearwater-fl/
Creditos Pequenos Online Calculadora Para Prestamos Personales El Credito Solicitud De Credito Donde Pedir Un Credito Rapido

5. Credito Dinero Rapido Prestamos Por Pagar Prestamos Con Poco Interes Consultar Prestamos Personales Necesito Un Prestamo De Dinero
https://elprestamista.space/el-cajon-ca/
Credito De Consumo Credito Rapido Web Calcular Cuota Prestamo Simulador De Prestamos Personales
https://elprestamista.space/pomona-ca/
Prestamo De Dinero Urgente Prestamos Baratos Prestamos Personales Express
https://elprestamista.space/east-point-ga/
Dinero Rapido Online Agencias De Prestamos De Dinero Prestamos De Dinero Con Dni

6. Solicitud De Credito Como Funcionan Los Prestamos Personales A Credito Calcular Prestamo Online Como Conseguir Un Credito Rapido
https://prestamosurgente.space/victoria-tx/
Donde Puedo Pedir Un Prestamo Personal Empresas Que Prestan Dinero Requisitos Para Un Credito Personal
https://prestamosurgente.space/fremont-ca/
Como Dinero Rapido Calcular Prestamo Online Calcular Cuota Prestamo Personal Dinero Credit
https://prestamosurgente.space/hayward-ca/
Oficinas De Prestamos De Dinero Donde Pedir Un Prestamo Personal Rapido Necesito Prestamo De Dinero Urgente

7. Microprestamos Prestamos Pequenos Y Rapidos Prestamo Express Creditos Personales Baratos
https://elprestamista.space/columbus-ga/
Necesito Un Credito Personal Lugares Donde Hacen Prestamos Personales Financieras De Creditos Personales Pedir Credito Rapido
https://elprestamista.space/miami-fl/
Solicitud De Dinero Mini Prestamos Inmediatos Prestamos A Plazos Prestamos Personales Sin Bancos
https://elprestamista.space/atascocita-tx/
Quien Me Puede Prestar Dinero Facil Y Rapido Creditos Personales Urgentes Micro Prestamos Online

8. Donde Puedo Solicitar Un Prestamo Rapido Creditos Y Prestamos Online Prestamos En Linea Credito 24 Horas
https://prestamosurgente.space/edison-nj/
Simulador Credito Nomina Facil Prestamos Dinero Facil Y Rapido Prestamos Personales Urgentes
https://prestamosurgente.space/lakewood-nj/
Pedir Credito Personal Prestamo Minicreditos Rapidos Online Prestamos De Dinero Inmediato Prestamos Personales En Estados Unidos
https://prestamosurgente.space/midland-tx/
Donde Hacer Un Prestamo Personal Prestamos Personales Prestamistas Simulador Prestamos Personales Online Mini Creditos On Line Creditos De Dinero

9. Credito De 300 Euros Los Prestamos Micro Prestamos Online
Mas Prestamos Contrato De Prestamo De Dinero Comparador De Prestamos Personales Online
Prestamos Rapidos Y Seguros Como Obtener Un Credito Personal Simulador Credito Personal Entidades De Prestamos De Dinero Prestamos A Corto Plazo
Como Pedir El Prestamo De Personal Credit Opiniones Tipo De Interes Actual Para Prestamos Personales Prestamos A Pagar Por Semana Como Solicitar Un Prestamo Personal

10. Simulador De Prestamos Minicreditos Online Simulador De Credito Online Companias De Prestamos Sacar Prestamo Personal
https://elprestamista.space/el-monte-ca/
Para Pedir Un Prestamo Pedir Prestamo Rapido Y Facil Creditos Baratos Mini Prestamos Personales Prestamo De Personal
https://elprestamista.space/west-covina-ca/
Requisitos Para Obtener Un Prestamo Personal Creditos Y Prestamos Personales On Line Prestamos Rapidos Y Faciles En Linea Credito Dinero Pedir Dinero Urgente
https://elprestamista.space/newnan-ga/
Tipos Prestamos Personales Creditos En Linea Tasa Para Prestamos Personales

11. Contrato De Prestamo De Dinero Prestamos Personales En 24 Horas Donde Puedo Pedir Un Prestamo De Dinero Prestamos Con Nomina Mini Creditos On Line
Microcreditos Rapidos Minicreditos Urgentes Prestamo 300 Euros Dinero En 24 Horas Prestamos En Linea
Mini Prestamos Creditos Rapidos Al Instante Prestamos Personales Express Quiero Sacar Un Prestamo Personal Creditos Por Internet Rapidos
$${}$$