Question

A piece of cloth costs Rs.70. If the piece is 4 metres longer and each metre costs Rs.2 less, the cost remains unchanged. The length of the piece is

• A. 8 m
• B. 9 m
• C. 10 m
• D. 12 m

Hint:

Translate “cost unchanged” into two equations $Lp=\text{const}$ and $(L+\Delta L)(p-\Delta p)=\text{same const}$; eliminate with $Lp$ to get a single relation.

Answer 1

The Correct Option is C

Step 1 (Variables): Let length $=L$ m, rate $=p$ Rs/m. Given $Lp=70$.
Step 2 (Second condition): $(L+4)(p-2)=70$. Expand using $Lp=70$:
$Lp-2L+4p-8=70 \Rightarrow 70-2L+4p-8=70 \Rightarrow -2L+4p-8=0$.
Step 3 (Relate $L,p$): $2p-L=4 \Rightarrow L=2p-4$. Substitute into $Lp=70$:
$p(2p-4)=70 \Rightarrow 2p^2-4p-70=0 \Rightarrow p^2-2p-35=0$.
Step 4 (Solve): $(p-7)(p+5)=0 \Rightarrow p=7$ (positive). Then $L=2\cdot7-4=\boxed{10\ \text{m}}$.
\textit{Check:} $10\times7=70$ and $(14)\times5=70$.