10th Maths 3.1

Exercise 3.1

Q1. Aftab tells her daughter,'' Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be''(Is not this interesting?) Represent this situation algebraically and graphically.

Sol. :

Let the present age of Aftab

= x

$=x$ years,

the present age of his daughter

= y

$=y$ years,

According to question

(x - 7) = 7 (y - 7)

$(x-7)=7(y-7)$

x - 7 = 7 y - 49

$x-7=7y-49$

x - 7 y + 42 = 0

$x-7y+42=0$

and after

3

$3$ years

(x + 3) = 3 (y + 3)

$(x+3)=3(y+3)$

x + 3 = 3 y + 9

$x+3=3y+9$

x - 3 y - 6 = 0

$x-3y-6=0$

For graphical representation,

x - 7 y + 42 = 0

$x-7y+42=0$

x = 7 y - 42

$x=7y-42$

when

x = 0

$x=0$

0 = 7 y - 42

$0=7y-42$

7 y = 42

$7y=42$

y = 6

$y=6$

When

x = 7

$x=7$

7 = 7 y - 42

$7=7y-42$

7 y = 42 + 7

$7y=42+7$

7 y = 49

$7y=49$

y = 7

$y=7$

X	0	7
y	6	7

and

x - 3 y - 6 = 0

$x-3y-6=0$

when

x = 0

$x=0$

0 - 3 x - 6 = 0

$0-3x-6=0$

3 x = - 6

$3x=-6$

x = - 2

$x=-2$

When

x = 6

$x=6$

6 - 3 y - 6 = 0

$6-3y-6=0$

- 3 y = 0

$-3y=0$

y = 0

$y=0$

X	0	6
y	-2	0

Answer :

Algebraically the two situations can be represented as follow

x - 7 y + 42 = 0, x - 3 y - 6 = 0

$x-7y+42=0, x-3y-6=0$

☝

Like, Share, and Subscribe.

Q2. The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 3 more balls of the same kind for ₹ 1300. Represent this situation algebraically and geometrically.

Sol. :

Let the cost price of each bat

x

$x$ ,

and the cost price of each ball

y

$y$ .

According to question

3 x + 6 y = 3900

$3x+6y=3900$

x + 2 y = 1300

$x+2y=1300$

and

x + 3 y = 1300

$x+3y=1300$

For geometrically (graphically) representation

x + 2 y = 1300

$x+2y=1300$

x = 1300 - 2 y

$x=1300-2y$

When

x = 300

$x=300$

300 = 1300 - 2 y

$300=1300-2y$

2 y = 1300 - 300

$2y=1300-300$

y = \frac{1000}{2}

$y=1000/2$

y = 500

$y=500$

When

x = 500

$x=500$

500 = 1300 - 2 y

$500=1300-2y$

2 y = 1300 - 500

$2y=1300-500$

2 y = 800

$2y=800$

y = \frac{800}{2}

$y=800/2$

y = 400

$y=400$

X	300	500
y	500	400

and

x + 3 y = 1300

$x+3y=1300$

x = 1300 - 3 y

$x=1300-3y$

When

x = 400

$x=400$

400 = 1300 - 3 y

$400=1300-3y$

3 y = 1300 - 400

$3y=1300-400$

3 y = 900

$3y=900$

y = \frac{900}{3}

$y=900/3$

y = 300

$y=300$

When

x = 100

$x=100$

100 = 1300 - 3 y

$100=1300-3y$

3 y = 1300 - 100

$3y=1300-100$

3 y = 1200

$3y=1200$

y = \frac{1200}{3}

$y=1200/3$

y = 400

$y=400$

X	400	100
y	300	400

Answer :

Algebraically the two situations can be represented as follow

x + 2 y = 1300, x + 3 y = 1300 .

$x+2y=1300, x+3y=1300.$

Q3 The cost of 2 kg of apples on a day was found to be ₹ 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is ₹ 300. Represent the situation algebraically and geometrically.

Sol. :

Let the cost price of

1 k g

$1kg$ of apples is

x

$x$ ,

and the cost price of

1 k g

$1kg$ of grapes is

y

$y$ .

According to question

2 x + y = 160

$2x+y=160$

and

4 x + 2 y = 300

$4x+2y=300$

2 x + y = 150

$2x+y=150$

when

x = 50

$x=50$

2(50)+y=160`

100 + y = 160

$100+y=160$

y = 160 - 100

$y=160-100$

y = 60

$y=60$

when

x = 60

$x=60$

2 (60) + y = 160

$2(60)+y=160$

120 + y = 160

$120+y=160$

y = 160 - 120

$y=160-120$

y = 40

$y=40$

X	50	60
y	60	40

and

2 x + y = 150

$2x+y=150$

when

x = 50

$x=50$

2 (50) + y = 150

$2(50)+y=150$

100 + y = 150

$100+y=150$

y = 150 - 100

$y=150-100$

y = 50

$y=50$

when

x = 60

$x=60$

2 (60) + y = 150

$2(60)+y=150$

120 + y = 150

$120+y=150$

y = 150 - 120

$y=150-120$

y = 30

$y=30$

X	50	60
y	50	30

Answer :

Algebraically the two situations can be represented as follow

2 x + y = 150, 2 x + y = 160

$2x+y=150, 2x+y=160$ .

Search This Blog

10th Maths 3.1

NCERT Class 10th solution of Exercise 3.2

NCERT Class 10th solution of Exercise 3.3

NCERT Class 10th solution of Exercise 3.4

NCERT Class 10th solution of Exercise 3.5

NCERT Class 10th solution of Exercise 3.6

NCERT Class 10th Maths Projects

Exercise 3.1

Comments

Popular posts from this blog

10th Maths Chapter 1

MPBSE 10th & 12th Result

CBSE 10th and 12th Result