Question

A piece of cloth cost Rs 5000. If the cost price of the cloth was Rs 5 less per meter, SOm more of the cloth would have been purchased. Find the cost price per meter of cloth and length of the cloth purchased. 

Answer 1

Let the cloth meters purchase initially was a meters.

Then , Cost per meter = `5000/"a"`

New cost per meter = `5000/("a" - 5)` , which enabled to buy 50 meter more.

⇒ In new condition, (Cost per meter) x (total length)= total cost `(5000/"a" - 5)("a" + 50) = 5000`

⇒ (5000 - 5a) (a + 50)= 5000 a 

⇒ 5000 a + 250000 - 5a² - 250a = 5000a 

⇒ 5a² + 250 a - 250000 = 0 

⇒ a² + 50 a - 500000 = 0 

⇒ a² + 250 a - 200a - 500000 = 0 

⇒ a (a + 250) - 200 (a + 250) = 0 

⇒ (a + 250)(a - 200) = 0 

⇒ a = 200 Meters .

⇒ Cost per meter = 5000/ 200 = Rs 25 / meter

Hence answer is Rs 25/ meter and 200 meters.