Question

Two articles $A$ and $B$ are sold for Rs. $1,167$ making $5\%$ profit on $A$ and $7\%$ profit on B. If the two articles are sold for Rs. $1,165$, a profit of $7\%$ is made on $A$ and a profit of $5\%$ is made on $B$. Find the cost price of each article.

• A. $A=$ Rs. $200$ and $B=$ Rs. $300$
• B. $A=$ Rs. $600$ and $B=$ Rs.$700$
• C. $A=$ Rs.$100$ and $B=$ Rs.$200$
• D. $A=$ Rs. $500$ and $B=$ Rs. $600$

Answer 1

The correct option is D $A=$ Rs. $500$ and $B=$ Rs. $600$

Let the cost price of $A=$ Rs. $x$ and that of $B=$ Rs. $y$
Given,
They are sold for Rs. $1,167$ making $5\%$ profit on $A$ and $7\%$ profit on $B$
$\Rightarrow 1.05x+1.07y=1167$ ------ $\left(1\right)$
Also, when the two articles are sold for Rs. $1,165$ a profit of $7\%$ is made on $A$ and a profit of $5\%$ is made on $B$.
$\Rightarrow 1.07x+1.05y=1165$ ------ $\left(2\right)$
Multiplying equation $\left(1\right)$ with $1.07$ we get, $1.1235x+1.1449y=1248.69$ ----- equation $\left(3\right)$

Multiplying equation $\left(2\right)$ with $1.05$ we get, $1.1235x+1.1025y=1223.25$ ----- equation $\left(4\right)$

Subtracting equation $\left(4\right)$ from $\left(3\right)$, we get $0.0424y=25.44\Rightarrow y=600$

Substituting $y=600$ in the equation $\left(2\right)$, we get $1.07x+1.05\left(600\right)=1165\Rightarrow x=500$
Hence, cost price of $A$ is Rs. $500$ and of $B$ is Rs. $600$