The total cost of 6 books and 7 pens is 79 rupees and the total cost of 7 books and 5 pens is 77 ruppees. Find the cost of 1 book and 2 pens.

Let the cost of one book be 'x' rupees and cost of one pen be 'y' rupees.

Cost of 6 books and 7 pens = 79 Rs

⇒ 6x + 7y = 79 eq.[1]

Cost of 7 books and 5 pens = 77 Rs

⇒ 7x + 5y = 77 eq.[2]

Multiplying eq.[1] by 5 both side, and Multiplying eq.[2] by 7 both side, we get

⇒ 30x + 35y = 395 eq.[3]

⇒ 49x + 35y = 539 eq.[4]

Subtracting eq.[3] from eq.[4], we get

⇒ 49x + 35y - 30x - 35y = 539 - 395

⇒ 19x = 144

Using this in eq.[1]

⇒ 864 + 19×7y = 79×19

⇒ 19×7y = 79×19 – 864

⇒

⇒ y = 5

& 6x + 7y = 79

⇒ 6x + 35 = 79

⇒ 6x = 44

⇒ x = 7

Hence, the cost of 1 pen & 2 books = Rs 1(y) + 2x

= 5 + 14 = Rs 19.