Question

If 7% of the sale price of an article is equivalent to 8% of its cost price and 9% of its sale price exceeds 10% of its cost price by Rs.1, then what is the cost of the article?
(a) Rs.400
(b) Rs.350
(c) Rs.300
(d) Rs.280

Answer 1

Hint: In the given question two relations are given between sales price and cost price hence we need to make the two equations involving two variables sales price and cost price and solve them to find both variables. To solve this question, assume the cost price and sale price as any two different random variables and make equations using those variables and relation given in the question and solve for those variables to get the value of cost price and sale price.

Complete step-by-step answer:
Suppose the cost price of the article is Rs. $ x $ and,
Suppose the sale price of the article is Rs. $ y $
Now according to question, 7% of the sale price of an article is equivalent to 8%,
\[7\%\text{ }of\text{ }y\text{ }=\text{ }8\%\text{ }of\text{ }x\]
Hence,
 $ \begin{align}
  & \dfrac{7}{100}y=\dfrac{8}{100}x \\
 & \\
\end{align} $
 $ 7y=8x $
 $ y=\dfrac{8x}{7}......(1) $
And also 9% of its sale price exceeds 10% of its cost price by Rs.1,
\[9\%\text{ }of\text{ }y=10\%\text{ }of\text{ }x\text{ }+\text{ }1~\]
Hence,
\[\dfrac{9}{100}y=\dfrac{10}{100}x+1\]
\[9y=10x+100......(2)\]
Putting the value of $ y=\dfrac{8x}{7} $ from equation (1) in equation (2) we get,
 $ 9\times \dfrac{8x}{7}=10x+100 $
 $ 72x=70x+700 $
Now taking 70x to the L.H.S of the equation, we get
 $ \begin{align}
  & 72x-70x=100 \\
 & 2x=700 \\
 & x=350 \\
\end{align} $
Putting the value x=350 in equation (1), we get
 $ \begin{align}
  & y=\dfrac{8\times 350}{7} \\
 & y=8\times 50 \\
 & y=400 \\
\end{align} $
Hence the value of $ x $ is 350 which is the value of cost price and value of $ y $ is 400 which is the sale price of the article.
So, the correct answer is “Option B”.

Note: whenever you are solving questions which involve statements, always try to convert those statements into equations with variables. It will make you see the problem in a very easy way and you will be able to solve it easily.Whenever you are making equations from the statements try to go line by line and try to understand what that line wants to convey. It is very easy to make wrong equations and hence end up with the wrong answer. For example in this question, when it is mentioned that “9% of its sale price exceeds 10% of its cost price by Rs.1” some students may end up making equation like this,
\[\dfrac{9}{100}y=\dfrac{10}{100}x-1\]which is wrong as the sale price is exceeding the cost price by Rs.1 and not ‘less than’ cost by Rs.1 so, Rs1 should be added to the equation and not subtracted.