3 pencils and 5 pens together cost Rs. 81, whereas 5 pencils and 3 pens together costs Rs. 71. The cost of 1 pencil and 2 pens together is:

Correct option is D

Given:

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

From the problem, we have the following equations:
1. 3x + 5y = 81
2. 5x + 3y = 71

Solution:

Eliminate one variable.
Multiply the first equation by 5 and the second equation by 3 to align the coefficients of x
( 15x + 25y = 405 ) …….1,

( 15x + 9y = 213 )……..2

Step 2: Subtract the second equation from the first:
 (15x + 25y) - (15x + 9y) = 405 - 213

16y = 192

y = 12

Substitute   y = 12  into the first equation:
3x + 5(12) = 81 

3x + 60 = 81

3x = 21

x = 7 

Then,  the cost of 1 pencil and 2 pens:
Cost = x + 2y

Cost = 7 + 2(12) = 7 + 24 = 31