The cost of 15 pens and 6 pencils is ₹291. If the cost of a pen decreases by ₹9 and the cost of a pencil increases by ₹2, then the cost of 9 pens and 3 pencils is ₹75. What is the original cost of 12 pens and 3 pencils?​

Correct option is D

Given:

Cost of 15 pens and 6 pencils = ₹291

New cost: Pen decreases by ₹9, Pencil increases by ₹2

Then, cost of 9 pens and 3 pencils = ₹75

Solution:

Let the original cost of a pen be x and a pencil be y

From first condition:

15x + 6y = 291 ...........(1)

From second condition (new prices):

9(x - 9) + 3(y + 2) = 75

9x - 81 + 3y + 6 = 75

9x + 3y = 150 ...........(2) 

subtracting 2$$\times$$eqn(2) - eqn(1)

$$18x +6y = 300 \\ \underline{-15x-6y=-291}\\ 3x\quad =\quad 9 \\ x \quad = \quad 3$$ 

Substitute x = 3 into (2):

3y = 150 − 9(3) =123

y = 41

Now, cost of 12 pens and 3 pencils:

= 12x + 3y = 12(3) + 3(41) = 36 + 123 = ₹159