Question

A 20%reduction in the unit cost of an articleenables one to buy 25 items more for 1000 .What is the original price of the item

Answer 1

The original price of the item is Rs1250

Answer 2

Answer:

The original price is Rs.10.

Step-by-step explanation:

Given : A 20%reduction in the unit cost of an article enables one to buy 25 items more for 1000 .

To find : What is the original price of the item?

Solution :

Let us assume original cost of item be x

According to question,

There is reduction of 20% in the unit cost

So,

Now the new unit cost = x - 20% of x

$=x-\frac{1}{5}x=\frac{4}{5}x$

Now let us assume that

For Rs. 1000 , the number of items bought be y

Then,

1000 = (initial price of items) * (Number of items bought)

1000 = xy  [ Eqn 1 ]

According to question,

From the same amount of money, ( y + 25 ) items can be bought

1000 = ( New unit price of items ) * ( New number of items )

1000 = 4/5( y + 25 )  [Eqn 2 ]

Substituting y from 1st equation in the 2nd, we get :

$1000=\frac{4}{5}[\frac{100}{x}+25]$

$1000\times 5=4000+100x$

$1000 = 100x$

$x=10$

Therefore, The original price is Rs.10.