Question

5 pens and 6 pencils together cost Rs.9 and 3 pens and 2 pencils cost Rs.5. Find the cost of 1 pen and 1 pencil.

Answer 1

 

Let the cost of 1 pen be x and that of 1 pencil be y.

$5x+6y=9\ \ \ \longrightarrow\ \ \ (1) \\ \\ 3x+2y=5\ \ \ \ \ \longrightarrow\ \ \ \ \ (2) \\ \\ \\ (1)+(2) \\ \\ \Rightarrow\ (5x+6y)+(3x+2y)=9+5 \\ \\ \Rightarrow\ 8x+8y=14 \\ \\ \Rightarrow\ 8(x+y)=14 \\ \\ \Rightarrow\ x+y=\bold{1.75} \\ \\ \\ Thank you. :-))$

     

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Assumption

Cost of a pen be Rs p

Also,

Pencil be Rs t

So,

5p + 6t = 9 ……..….(1)

3p + 2t = 5 ...........(2)

Here,

Multiply (1) by 2 also (2) by 6 we get,

10p + 12t = 18 ……..…(3)

18p + 12t = 30 ……..…(4)

Here,

Subtract (3) by (4),

8p = 12

p = 12/8

p = 3/2

Putting value of p in (1),

5p + 6t = 9

5 × 3/2 + 6t = 9

15/2 + 6t = 9

6t = 9 - 15/2

6t = [18 - 15]/2

6t = 3/2

t = 3/2 × 1/6

t = 1/4

Therefore,

Cost of one pen is Rs. 3/2

Cost of one pencil is Rs. 1/4