Question

5 pencils and 7 pens together cost ₹ 195 while 7 pencils and 5 pens together cost ₹ 153. Find the cost of each one of the pencil and the pen.

Answer 1

Given: Let cost of one pencil = x (₹) and one pen = y (₹). Then 5x + 7y = 195 and 7x + 5y = 153.

Step-wise calculation:

1. Add the two equations:

(5x + 7y) + (7x + 5y) = 195 + 153

⇒ 12x + 12y = 348

⇒ x + y = 29

2. From x + y = 29, we get y = 29 – x. 

Substitute into 5x + 7y = 195:

5x + 7(29 – x) = 195

⇒ 5x + 203 – 7x = 195

⇒ –2x = –8 

⇒ x = 4

3. Then y = 29 – x 

= 29 – 4

= 25

Cost of one pencil = ₹ 4 and cost of one pen = ₹ 25.