Question

A 20 reduction in the unit cost of an article enables one to buy 25 items more for rs 1000

Answer 1

Answer:initially the rate was 40 rs.

Step-by-step explanation:

let initially the price of an item x rs.

after reduction of 20 rs. he can buy 25 more items.

so

$\frac{1000}{x-20}-\frac{1000}{x}=25\\\\\frac{1000x-1000x+20000}{x(x-20)}=25\\\\\frac{20000}{x^{2}-20x}=25\\\\800=x^{2}-20x\\\\x^{2}-20x-800=0\\\\(x-40)(x+20)=0$

x = 40 rs. because price can not be negative.

so initially he buy an item in 40 rs.

Answer 2

The original cost of the item would be Rs. 10

Explanation:

Let the original price of the item be x

Given that,

Reduction in its unit cost = 20%

= 20% of x

= x/5

Now,

The new unit cost would be x - x/5

= 4x/5

Let us assume that,

For every Rs. 1000, y items are bought

Thus,

1000 Rs. = Original price of the item * items bought

∵ $1000 = xy$  ...(i)

A.T.Q.

For the same amount, extra 25 units can be bought.

1000 = New unit price of items * New no. of items

∵ $1000 = 4/5( y + 25 )$ ...(ii)

By substituting the values of equation (i) in (ii),

$1000 = 4/5 (100/x + 25)$

$1000$ × $5 = 4000 + 100x$

⇒ $5000 - 4000 = 100x$

⇒ $1000 = 100x$

⇒ $x = 1000/100$

∵ $x = 10$

Thus, the original price is Rs. 10.

Learn more: Unit cost

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