Question

The cost of 5 pens and 8 pencils is ₹ 120, while the cost of 8 pens and 5 pencils is ₹ 153. Find the cost of 1 pen and that of 1 pencil.

Answer 1

Given: 5p + 8c = ₹ 120 and 8p + 5c = ₹ 153.

Step-wise calculation:

1. Subtract the first equation from the second:

(8p + 5c) – (5p + 8c) = 153 – 120

⇒ 3p – 3c = 33

⇒ p – c = 11

⇒ p = c + 11

2. Substitute p = c + 11 into 5p + 8c = 120:

5(c + 11) + 8c = 120

⇒ 5c + 55 + 8c = 120

⇒ 13c = 65

⇒ c = 5

3. Then p = c + 11

= 5 + 11 

= 16

Cost of 1 pen = ₹ 16; cost of 1 pencil = ₹ 5.