Question

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

Answer 1

Answer :

10m

Step-by-step explanation:

Let the length of the cloth be x .

It is given that the cloth costs ₹35 .

⇒ cost of 1 m cloth is 35/x .

Now the given condition is that length of cloth is 4m more .

⇒ new length =x+4 .

Next condition is cost of each /1m is 1 less

⇒ new cost of 1m = 35/x-1 .

and it also says that the price remains unchanged  .

new cost of 1m × new length of cloth = total cost

⇒ (35/x - 1)(x + 4 ) = ₹ 35

⇒ (35-x)(x+4)=35×x

⇒ 35x + 140 -x² -4x = 35x

⇒ x² +4x -140 =0

⇒ x² +14x - 10x -140 =0

⇒ x( x+14 ) -10( x +14 ) =0

⇒ (x +14) ( x - 10 ) =0

⇒ x=-14 , x=10 .

But x= length and can't be negative  .

⇒ x = 10m .

∴ The length of the cloth is 10 m  .