Question

The ratio of selling price of article $A,B,C$ is $8:9:5$ and ratio of percentage profit is $8:7:14$ respectively. If the profit percentage of $A$ is $14.28\%$ and the cost price of $B$ is Rs. $400$. What is the overall percentage gain?

• A. $14.87$
• B. $16.66$
• C. $14.28\%$
• D. $15.78\%$
• E. None of these

Answer 1

The correct option is D $15.78\%$

Selling price of article $A,B$ and $C$ is in ratio $8:9:5$
Let Selling price is $8y,9y$ and $5y$
Profit percentage in ratio $=8:7:14$
Let their profit percentage is,
$8x\%,7x\%$ and $14x$
A's profit percent $=14.28\%$
$8x\%=14.28\%$
$x=\frac{14.28}{8}=1.78$
$B^{\prime }s$ Profit percent,
$=7x\%=7\times 1.78=12.50\%$ (approx)
$C^{\prime }s$ profit percentage $=14x=14\times 1.78=25\%$
Cost price of $B=$ Rs. $400$
$\therefore$ Selling price ofB = $400+\frac{12.50}{100}\times 400=$ Rs. $450$
$\therefore 9y=450$
$y=50$
Selling price of $A$ $=8y=8\times 50=$ Rs. $400$
SP of $C$ $=5y=5\times 50=$ Rs. $250$
Total SP $=450+400+250=$ Rs. $1100$
Let CP of $A=a$
$a=400-14.28\%$ of $a$
$a=400-\frac{14.28a}{100}$

$100a=40000-14.28a$
$114.28a=40000$
$a=$ Rs. $350$
Let CP of $C=c$
$c+25\%$ of $c=250$
$125c=25000$
$c=$ Rs. $200$
Total CP $=400+350+200=$ Rs. $950$
Profit $=1100-950=150$
Overall $\%$ profit $=\frac{150}{950}\times 100=15.78\%$