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A piece of cloth costs Rs 200 .If the piece were 5m longer, and each metre of cloth costed Rs 2 less the cost of the piece would have remained unchanged. How long is the piece and what is its original rate per metre.

The ans. is 20m & Rs.10. pls give me the steps

let the length of the cloth be x and cost of cloth per m be y then,

x * y = 200

  so, y = 200/x  ....(1)

now, If the piece were 5m longer, and each metre of cloth costed Rs 2 less, then,

(x+5)(y -2) = 200.

xy -2x + 5y -10 = 200

putting the value of (1), we get,

1000/x - 2x = 200 - 190

1000 -2x2 = 10x

500 -x2 = 5x

x2+5x - 500 = 0

x2 +25x -20x -500 =0

x(x+25) -20(x+25) = 0

(x-20) (x+25) = 0

so, x= 20m  (neglecting x= -25)

so, y = 200/x = 200/20

  = 10 Rs....ans.... :)



 

  • 95
View Full Answer

 Hi....

Let the length of the piece be x m.

Then, cost per metre = 

New length = (x + 5) m

Since, the cost of piece of cloth remain unchanged.

∴ New cost per metre = 

Now, 

As x cannot be negative. So, x = 20

∴ Cost per metre = 

Hence, the length of the piece of cloth is 20 m and cost is Rs 10 per metre.

 

Cheers!!

 

 
  • 59
Let the cost of cloth per metre be x . Total cost =200rs. Cloth in metre=200/x.Now,if cloth was 5m longer then total cloth=200/x+5. acc.to ques...... 200/(x+5) = (200/x)-2. by solving the given equation.......we can get the answer i.e.,20m long and cost =10 rs per metre
  • 10

let the length of the cloth be x and cost of cloth per m be y then,

x * y = 200

so, y = 200/x ....(1)

now, If the piece were 5m longer, and each metre of cloth costed Rs 2 less, then,

(x+5)(y -2) = 200.

xy -2x + 5y -10 = 200

putting the value of (1), we get,

1000/x - 2x = 200 - 190

1000 -2x2 = 10x

500 -x2 = 5x

x2+5x - 500 = 0

(x-20) (x+25) = 0

so, x= 20 (neglecting x= -25)

so, y = 200/x = 200/20 = 10

Hence, the length of the piece of cloth is 20 m and rate per metre is Rs 10.
hope it is helpful

  • 9
Go see in the top
  • -4
let the length of the cloth be x and cost of cloth per m be y then,

x * y = 200

? so, y = 200/x? ....(1)

now, If the piece were 5m longer, and each metre of cloth costed Rs 2 less, then,

(x+5)(y -2) = 200.

xy -2x + 5y -10 = 200

putting the value of (1), we get,

1000/x - 2x = 200 - 190

1000 -2x2?= 10x

500 -x2?= 5x

x2+5x - 500 = 0

x2?+25x -20x -500 =0

x(x+25) -20(x+25) = 0

(x-20) (x+25) = 0

x = 20
  • 2
Let the piece of cloth is x metre and it costs Rs.y/metre. Then by the given conditions -
∴, xy=200 -------------(1) and
(x+5)(y-2)=200
or, xy+5y-2x-10=200
or, 200+5y-2x-10=200
or, 5y-2x-10=0
or, 5y=2x+10
or, y=(2x+10)/5
Putting in (1),
x(2x+10)/5=200
or, x(2x+10)=200×5
or, 2x²+10x=1000
or, x²+5x-500=0
or, x²+25x-20x-500=0
or, x(x+25)-20(x+25)=0
or, (x+25)(x-20)=0
either, x+25=0
or, x=-25
or, x-20=0
or, x=20
Since the length of the cloth can not be negative,
∴, x=20 metre
Putting in (1),
20y=200
or, y=10
∴, the cloth is 20 m long and the original rate is Rs. 10/metre. 









































































































































 
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