Question

The cost of 5 pens and 8 pencils is ₹120, while the cost of 8 pens and 5 pencils is ₹153.
Find the cost of 1 pen and that of 1 pencil.

Answer 1

Let the cost of 1 pen and 1 pencil are ₹x and ₹y respectively.
Then as per the question
$$\begin{gathered} 5x+8y=120.....\left(i\right) \\ 8x+5y=153.....\left(ii\right) \end{gathered}$$
Adding (i) and (ii), we get
$$\begin{gathered} 13x+13y=273 \\ \Rightarrow x+y=21.....\left(iii\right) \end{gathered}$$
Subtracting (i) from (ii), we get
$$\begin{gathered} 3x-3y=33 \\ \Rightarrow x-y=11.....\left(iv\right) \end{gathered}$$
Now, adding (iii) and (iv), we get
$2x=32\Rightarrow x=16$
Substituting x = 16 in (iii), we have
$16+y=21\Rightarrow y=5$
Hence, the cost of 1 pen and 1 pencil are respectively ₹16 and ₹5.