A piece of cloth costs Rs. 35. If the piece were 4 m longer and each metre costs Rs. 1 less, the cost would remain unchanged. How long is the piece?

Question

Philoid · Accepted Answer

Let the length of cloth be ‘a’ m.

Given, piece of cloth costs Rs. 35 and if the piece were 4 m longer and each metre costs Rs. 1 less, the cost remains unchanged.

Cost of 1m of cloth = 35/a

⇒ (a + 4)(35 – a) = 35a

⇒ 35a + 140 – a² – 4a = 35a

⇒ a² + 4a – 140 = 0

⇒ a² + 14a – 10a – 140 = 0

⇒ a(a + 14) – 10(a + 14) = 0

⇒ (a – 10)(a + 14) = 0

⇒ a = 10 m