Question

A dishonest shopkeeper pretends to sell his goods at cost price but uses false weights and gains $11\frac{1}{9}$ $\%$. For a weight of $1$ kg he uses

• A. a weight of $875$ gm
• B. a weight of $900$ gm
• C. a weight of $950$ gm
• D. a weight of $850$ gm

Answer 1

Answer: (B)

a weight of $900$ gm

Let the error (difference between $1$ kg and false weight) be $x$ gm.

Then $\frac{x}{(1000-x)}\times 100=\frac{100}{9}$

$\Rightarrow \frac{x}{(1000-x)}=\frac{1}{9}$
$\Rightarrow$ $9x=1000-x$

$\Rightarrow$ $10x=1000$

$\Rightarrow$ $x=100$
$\therefore$ Weight used $=(1000-100)$ gm $=900$ gm