Question

A pice of cloth costs Rs. 35 , if the pice were 4 m longer and each meter were to cost Rs. 1 lesser , then the total cost would remain unchanged. How is the pice of cloth?

Answer 1

Let the cost of x cost = Rs. 35

& y be the cost of 1m cloth

Therefore,

xy = 35

y = 35/x

According to the question,

$(x+4)(y-1)=35$

$(x+4)(\frac{35}{x-1}) = 35$

$(x\times \frac{35}{x}) -x + (4 \times \frac{35}{x}) -4 = 35$

$35 - x + \frac{140}{x} - 4 = 35$

${-x}^{2} + \frac{140 - 4x} {x} = 35 - 35$

${-x}^{2} + 140 - 4x = 0$

${x}^{2} + 4x - 140 = 0$

${x}^{2} + 14x - 10x - 140 = 0$

$x (x + 14) - 10 (x + 14) = 0$

$(x-10)(x+14) = 0$

$x = 10$

$y = \frac{35}{10} = 3.5$

Therefore,

10m cloth cost Rs. 35

and cost of 1m cloth is Rs. 3.5

Answer 2

$\rule{200}3$

$\Huge{\red{\underline{\textsf{Answer}}}}$

Let the length of the cloth = x meters.

Then xy = 35

and (x + 4)(y - 1) = 35

$\longrightarrow$ $\sf xy - x + 4y - 4 = 35$

$\longrightarrow$ $\sf -x + 4y = 4 \:since\: xy = 35$

$\longrightarrow$ $\sf x = 4y - 4 \mapsto y(4y - 4) = 35$

$\longrightarrow$ $\sf 4y^2 - 4y - 35 = 0$

$\pink\longrightarrow$ $\large\underline{\boxed{\pink{\sf y = \frac{7}{2} or \frac{-5}{2}}}}$ $\orange\star$

$\longrightarrow$ So $\sf x \frac{7}{2} = 35$

$\orange\longrightarrow$ $\large\underline{\boxed{\orange{\sf x = 10}}}$ $\pink\star$

$\rule{200}3$