Question

By selling toffees at a rate of $20$ for $Rs10$, a man loses $4\%$. To gain $20\%$, how many toffees must be sold for $Rs10$?

• A. $13$ toffees
• B. $16$ toffees
• C. $19$ toffees
• D. $22$ toffees

Answer 1

The correct option is B $16$ toffees

S.P. of $1$ toffee $=$ Rs. $\frac{10}{20}=$ Rs. $\frac{1}{2}$, Loss $=4\%$

$\therefore$ C.P. $1$ toffee $=$ $\frac{\frac{1}{2}\times 100}{(100-4)}=\frac{100}{2\times 96}=$ Rs. $\frac{25}{48}$

Now, C.P. $=$ Rs. $\frac{25}{48}$, Gain $=20\%$

$\therefore$ S.P. $=\frac{\frac{25}{48}\times (100+20)}{100}=\frac{25\times 120}{48\times 100}=$ Rs. $\frac{5}{8}$

Rs. $\frac{5}{8}$ is the S.P. of $1$ toffee.
$\therefore$ Rs. $10$ is the S.P. of $\frac{1}{5/8}\times 10=\frac{8\times 10}{5}=16$ toffees.