Question

A mobile vendor has 22 items, some which are pencils and others are ball pens. On a particular day, he is able to sell the pencils and ball pens. Pencils are sold for ₹ 15 each and ball pens are sold at ₹ 20 each. If the total sale amount with the vendor is ₹ 380, how many pencils did he sell?

Answer 1

Let vendor have ‘p’ number of pencils and ‘b’ number of ball pens

Given that the total number of items is 22

∴ p + b = 22 ........(1)

Pencils are sold for ₹ 15 each and ball pens for ₹ 20 each

Total sale amount = 15 × p + 20 × b

= 15p + 20b which is given to be 380.

∴ 15p + 20b = 380

Dividing by 5 throughout,

`(15"p")/5 + (20"b")/5 = 380/5`

⇒ – 3p + 4b = 76  .......(2)

Multiplying equation (1) by 3 we get

3 × p + 3 × b = 22 × 3

⇒ 3p + 3b = 66 .........(3)

Equation (2) – (3) gives

3p + 4b  = 76
(–)     (–)     (–)
3p + 3b  = 66
 0  +   b  = 10

∴ b = 10

∴ p = 12

He sold 12 pencils