The cost of 2 pens and 19 pencils is ₹118. If the cost of a pen decreases by ₹5 and the cost of a pencil increases by ₹4, then the cost of 5 pens and 8 pencils is ₹144. What is the original cost of 14 pens and 6 pencils?

Correct option is C

Given:

Cost of a pen = p

Cost of a pencil = c

2p + 19c = 118

After changes:

5(p - 5) + 8(c + 4) = 144

Find cost of (14p + 6c)

​Solution:​

2p + 19c = 118 .........(1)

Form second equation

5p - 25 + 8c + 32 = 144

5p + 8c + 7 = 144

5p + 8c = 137...... ...(2)

Multiply equation (1) by 5 and equation (2) by 2 and than Subtract (2) from (1)

(10p + 95c) - (10p + 16c) = 590 - 274

79c = 316

c = 4

Substituting (c = 4) in equation (2)

5p + 8(4) = 137

5p + 32 = 137

5p = 105

p = 21

Now,  cost of 14 pens and 6 pencils

14p + 6c = 14(21) + 6(4)

= 294 + 24 = ₹318