Simple Equations

priya11 · Joined: 23 Jan 2007 Posts: 3

At a certain Stationery Store,only four varieties of pens and only four varieties of pencils are sold.The price of a set of one of each of the four varieties of pens is Rs.45.The price of a set of one of each of the four varieties of pencils is Rs.12.The price of the cheapest pencil is Re.1 and the prices of three of the varieties of pens are exactly twice the prices of the other 3 varieties of pencils.What is the price of the costliest variety of pen?
1)Rs.24
2)Rs.23
3)Rs.22
4)None of these

Mramitkumarnain · Joined: 21 Jan 2007 Posts: 1

Let,
l1,l2,l3,l4 be the 4 pens
and
p1,p2,p3,p4 be the 4 pencils with p4 the least expensive

now given
p1+p2+p3+p4=12
also p4 = 1
hence,
p1+p2+p3=11
or 2*11=l1+l2+l3 = 22
also l1+l2+l3+l4 = 45
hence
l4=23 and it is very clear that this is the most expensive hence

Ans is 2 i.e Rs 23
if anyone has a better solution pls do post