Question

23 spoons and 17 forks together cost ₹1,770, while 17 spoons and 23 forks together
cost ₹1,830. Find the cost of a spoon and that of a fork.

Answer 1

Let the cost of a spoon be ₹x and that of a fork be ₹y. Then
$$\begin{gathered} 23x+17y=1770.....\left(i\right) \\ 17x+23y=1830.....\left(ii\right) \end{gathered}$$
Adding (i) and (ii), we get
$$\begin{gathered} 40x+40y=3600 \\ \Rightarrow x+y=90.....\left(iii\right) \end{gathered}$$
Now, subtracting (ii) from (i), we get
$$\begin{gathered} 6x-6y=-60 \\ \Rightarrow x-y=-10.....\left(iv\right) \end{gathered}$$
Adding (iii) and (iv), we get
$2x=80\Rightarrow x=40$
Substituting x = 40 in (iii), we get
$40+y=90\Rightarrow y=50$
Hence, the cost of a spoon that of a fork are ₹40 and ₹50 respectively.