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Home » 1. 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?
1. 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?
CBSE | Class 10 | Maths | Maths | Quadratic Equations | Quadratic Equations | RD Sharma
1. 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?

Solution:

Let’s assume the length of the cloth to be ‘a’ meters.

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

From the above condition, we have

Cost of 1m of cloth = 35/a

⇒ (a + 4)(35 - a) = 35a        

35a+140-{{\alpha }^{2}}-4a=35a

{{a}^{2}}+4a-140=0

Solving for ‘a’ by factorization method,

{{a}^{2}}+14a-10a-140=0           

⇒ a(a + 14) - 10(a + 14) = 0

⇒ (a - 10)(a + 14) = 0         

⇒ a = 10 m or a = -14 (neglected)

Since, the length of a cloth can never be negative.

So, a = 10

Hence, the piece of cloth was 10 m long.

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