Question

The cost of 4 pens and 4 pencil boxes is Rs 100. Three times the cost of a pen is Rs 15 more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pen and a pencil box

NCERT Class X
Mathematics - Exemplar Problems

Chapter _PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

Answer 1

Solution :-

Let the cost of a pen be Rs 'x' and the cost of a pencil box be Rs. 'y'

As, the cost of 4 pens and 4 pencil boxes is Rs. 100

So, 4x + 4y = 100 .................(1)

And, three times the cost of a pen is Rs. 15 more than the cost of a pencil box.

So, 3x = y + 15

⇒ 3x - y = 15 ......................(2)

Now multiplying the equation (1) by 3 and equation (2) by 4, we get

⇒ (4x + 4y = 100)*(3) = 12x + 12y = 300 ................(3)

⇒ (3x - y = 15)*(4) = 12x - 4y = 60 ..........................(4)

Now, subtracting (4) from (3)

  12x + 12y = 300
  12x -  4y   = 60 
 -      +         -
_________________
         16y = 240
_________________

⇒ 16y = 240

⇒ y = 240/16

⇒ y = 15

Now, substituting the value of y = 15 in (2)

⇒ 3x - y = 15

⇒ 3x - 15 = 15

⇒ 3x = 15 + 15

⇒ 3x = 30

⇒ x = 30/3

⇒ x = 10

So, the cost of a pen is Rs. 10 and the cost of a pencil box is Rs. 15

Answer.

Answer 2

let the number of pens be x and number of pencil boxes be y .

According to the question our first eq.4x+4y=100

and we have been told that 3 times the cost of pen is rs 15 more than the cost of a pencil box. So our second eq. will be 3x=15+y

multipying eq 2 by 4 we get 12x-4y= 6o

now eliminating 4x+4y=100

12x-4y=60

we get x=10 and y=15