UPSC CDS 1 2022 Math Paper

Given:
A piece of cloth costs Rs. 10,000
Concept used:
Total cost = total item × price of each item
Calculation:
Let at the beginning piece of cloth be xm
According to the question,
[10000∕x−10000∕(x+2)]=250
⇒[(10000x+20000−10000x)∕x(x+2)]=250
⇒[20000∕x(x+2)]=250
⇒20000=250x2+500x
⇒250x2+500x−20000=0
⇒x2+2x−80=0 [By dividing 250 from both side ]
⇒x2+10x−8x−80=0
⇒x(x+10)−8(x+10)=0
⇒(x+10)(x−8)=0
So, x=8 or −10
But x cannot be negative
∴ The original length of the piece of cloth is 8m