Question

The cost of 5 pens and 8 pencils together cost Rs. 120 while 8 pens and 5 pencils together cost Rs. 153. Find the cost of a 1 pen and that of a 1 pencil.

Answer 1

Let the cost of 1 pen and 1 pencil are Rs.x and Rs.y respectively.

Then as per the question

5x + 8y = 120 …….(i)

8x + 5y = 153 …….(ii)

Adding (i) and (ii), we get

13x + 13y = 273

⇒ x + y = 21 …….(iii)

Subtracting (i) from (ii), we get

3x – 3y = 33

⇒ x – y = 11 ………(iv)

Now, adding (iii) and (iv), we get

2x = 32

⇒ x = 16

Substituting x = 16 in (iii), we have

16 + y = 21

⇒ y = 5

Hence, the cost of 1 pen and 1 pencil are respectively Rs.16 and Rs.5.