Question

5 books and 7 pens together costs Rs. 79 whereas 7 books and 5 pens together cost Rs. 77. Find the cost of 1 book and 2 pens.

• A. Total price Rs. $30$
• B. Total price Rs. $20$
• C. Total price Rs. $15$
• D. Total price Rs. $22$

Answer 1

The correct option is B Total price Rs. $20$

Let the cost of a book Rs x and the cost of a pen Rs y.
Then, the equations formed are :
$5x+7y=79$ ....(i)
$7x+5y=77$ .....(ii)
On adding (i) and (ii) , we get
$12x+12y=156$
$\Rightarrow x+y=13$ ....(iii)
On subtracting (i) from (ii) , we get
$2x-2y=-2$
$\Rightarrow x-y=-1$ ....(iv)
On adding (iii) and (iv) , we get
$2x=12$
$\Rightarrow x=6$
By putting $x=6$ in (iv), we get
$6-y=-1$
$\Rightarrow y=7$
cost of 1 book and 2 pens = $x+2y=6+2\left(7\right)=Rs.20$