Question

A company spent 42,000 for buying
cooler. Since the price shot up by 500
per cooler, they got 2 coolers less.
(i) Find the original cost of a cooler.
(ii) Find the new price. (iii) How
many coolers did they buy? [4]​

Answer 1

(I) The orignal cost of the cooler is ₹ 3000.

(ii) The new price of the cooler is ₹ 3500.

(iii) The number of cooler they buy is 14.

Step-by-step explanation:

Given:

• A company spent 42,000 for buying
• cooler.
• The price shot up by 500
• per cooler, they got 2 coolers less.

Let the orignal price of cooler is ₹ x.

Let the number of cooler initially buy is y.

$= > xy = 42000 \: \: \: \: \: \: \: .....(1)$

After the price shot,

$= > (x + 500)(y - 2) = 42000 \\ = > xy + 500y - 2x - 1000 = 42000$

From equation (1) xy= 42000,

$= > 42000 + 500y - 2x - 1000 = 42000 \\ = > 2x = 500y - 1000 \\ = > x = 250(y - 2)$

Now put value of x in equation (1),

$= > 250 (y - 2) \times y = 42000 \\ = > {y}^{2} - 2y = 168 \\ = > {y}^{2} - 2y - 168 = 0 \\ = > (y - 14)(y + 12) = 0 \\ = > y = 14..y = - 12$

=> y =14 is valid

Putting value of y in value of x,

$= > x = 250(y - 2) \\ = > x = 250(14 - 2) \\ = > x = 250 \times 12 \\ = > x = 3000$

(I) The orignal cost of the cooler is ₹ 3000.

(ii) The new price of the cooler is ₹ 3500.

(iii) The number of cooler they buy is 14.