Question

23 spoons and 17 forks together cost Rs.1770,while 17 spoons and 23 forks together cost Rs.1830.Find the cost of a spoon and that of a fork.

Answer 1

Let spoon be x and fork be y

23 spoon and 17 forks together cost rs 1770
so, $23x+17y=1770$
$23x=1770-17y$
$x=\frac{1770-17y}{23}$............(1)

17 spoon and 23 forks together cost rs 1830
so, $17x+23y=1830$............(2)

substitute (1) in (2)
$17\left(\frac{1770-17y}{23}\right)+23y=1830\frac{(30090-289y+529y)}{23}=183030090+240y=42090240y=42090-30090240y=12000y=\frac{12000}{240}y=50$

substitute y in (1)
$x=\frac{1770-17\times 50}{23}x=\frac{(1770-850)}{23}x=\frac{920}{23}x=40$

so, the cost of the spoon is x = 40 rupees and the cost of the fork is y = 50