If 11 pens and 19 pencils together cost ₹ 502, while 19 pens and 11 pencils together cost ₹ 758, how much do 3 pens and 6 pencils cost together?

Let the cost of a pen be ₹ x and ₹ y be the cost of a pencil.

Given,

11 pens and 19 pencils together cost ₹ 502.

⇒ 11x + 19y = 502     ……..(1)

Given,

19 pens and 11 pencils together cost ₹ 758.

⇒ 19x + 11y = 758     ………(2)

Subtracting equation (1) from equation (2), we get :

⇒ 19x + 11y - (11x + 19y) = 758 - 502

⇒ 19x - 11x + 11y - 19y = 256

⇒ 8x - 8y = 256

⇒ 8(x - y) = 256

⇒ x - y = $\dfrac{256}{8}$

⇒ x - y = 32

⇒ x = 32 + y …..(3)

Substituting value of x in equation (1), we get :

⇒ 11x + 19y = 502

⇒ 11(32 + y) + 19y = 502

⇒ 352 + 11y + 19y = 502

⇒ 30y = 502 - 352

⇒ 30y = 150

⇒ y = $\dfrac{150}{30}$

⇒ y = ₹ 5.

Substituting value of y in equation (3), we get :

⇒ x = 32 + y

⇒ x = 32 + 5

⇒ x = ₹ 37.

The amount to buy the 3 pens and 6 pencils is,

⇒ 3x + 6y

⇒ 3 × 37 + 6 × 5

⇒ 111 + 30

⇒ ₹ 141.

Hence, 3 pens and 6 pencils costs ₹ 141.