The cost of 12 pens and 7 pencils is ₹285. If the cost of a pen decreases by ₹6 and the cost of a pencil increases by ₹5, then the cost of 11 pens and 3 pencils is ₹118. What is the original cost of 2 pens and 2 pencils?

Correct option is D

Given:

Cost of 12 pens and 7 pencils = ₹285

If pen price decreases by ₹6 and pencil price increases by ₹5, then cost of 11 pens and 3 pencils = ₹118

Find original cost of 2 pens and 2 pencils

​Solution:​

Let the original cost of:

1 pen = P and 1 pencil = Q

Now, 

12P + 7Q = 285.......(1) 

New prices: pen = (P - 6), pencil = (Q + 5)

11(P - 6) + 3(Q + 5) = 118

11P - 66 + 3Q + 15 = 118

11P + 3Q - 51 = 118

11P + 3Q = 169 ..........(2)

Subtracting equations 7 × (2) - 3×(1)

77P - 36P = 1183 - 855

41P = 328

P = 8

Substitute in (2):

11(8) + 3Q = 169

88 + 3Q = 169

3Q = 81

Q = 27

Original cost of 2 pens and 2 pencils:

2P + 2Q = 2(8) + 2(27) = 16 + 54 = ₹70