Question

A 20% reduction in the unit cost of an article enables one to buy 25 items more for Rs. 1000. What is the original unit cost of the item? a) 12 b) 8 c) 10 d) 15

Answer 1

10 is the original uni

Answer 2

Answer:

Original unit cost of item is ( d ) 10

Step-by-step explanation:

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 = x * y  [ Let this be Eqn 1 ]

Also,

According to question,

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

So,

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

1000 =  $\frac{4}{5}x$ * ( y + 25 )  [Let this be Eqn 2 ]

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

1000 = $\frac{4}{5}x$ * ( $\frac{1000}{x}+25$ )

1000 = $\frac{4}{5}x$ * ( $\frac{1000+25x}{x}$ )

1000 * 5 = 4000 + 100x

5000 - 4000 = 100x

1000 = 100x

x = 10

Hence,

Original unit cost of item is ( d ) 10