Question

A cricket bat is sold at a profit of 7%. Had it been sold for Rs.60 more, the profit percent would have been 12%. Find the cost price of the bat.

Answer 1

Hint: By knowing the formula of profit percentage, the problem can be solved. First write the formula of profit percentage as \[\Rightarrow \dfrac{SP-CP}{CP}\times 100\] and equate it with 7%, then, add 60 to the selling price and rewrite the formula of profit percentage and equate it with new profit % that is 12%. Solving these two equations the required cost price would come.

Complete step-by-step answer:
A cricket bat is sold at a profit of 7%. Profit is nothing but the gain any person would earn after selling any product at a cost higher than the price at which the person buys it or its original price.
So, according to the definition,
\[\text{Profit=Selling Price (SP) - Cost Price (CP)}\]
But, here, we are talking about profit %, which is,
Profit% \[\text{= }\dfrac{SP-CP}{CP}\times 100\]
Cricket ball is sold at 7% profit, so we can write the equation as
\[\begin{align}
  & 7=\dfrac{SP-CP}{CP}\times 100 \\
 & 0.07=\dfrac{SP-CP}{CP} \\
 & 0.07CP=SP-CP \\
 & SP=1.07CP\text{ }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. (1)} \\
\end{align}\]
We name this equation as (1).
If the ball had been sold for Rs.60 more than the earlier selling price, the profit% would have been 12%.
As per the question, we can write
\[SP'=SP+60\text{ }\left[ SP'=\text{ New selling price} \right]\]
So, now we get equation for profit% as,
Profit% \[\text{= }\dfrac{SP'-CP}{CP}\times 100\]
\[\Rightarrow 12=\] Profit % \[=\text{ }\dfrac{\left( SP'+60 \right)-CP}{CP}\times 100\]
\[\begin{align}
  & \Rightarrow 0.12=SP+60-CP \\
 & \Rightarrow SP+60=1.12CP\text{ }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. (2)} \\
\end{align}\]
We can name this equation as (2).
Now, subtract equation (1) from equation (2), we get
\[\begin{align}
  & \left( SP+60=1.12CP \right)-\left( SP=1.07CP \right) \\
 & \Rightarrow SP+60=1.12CP \\
 & -\left( SP \right)=-1.07CP \\
 & 60=0.05CP \\
 & 60=\dfrac{5}{100}CP \\
 & CP=\dfrac{60\times 100}{5} \\
 & CP=1200 \\
\end{align}\]
Therefore, CP= Rs.1200
Hence, original or cost price of the cricket bat is Rs.1200

Note: It is not necessary to subtract the equation formed, students can solve the two equations formed in the question by any convenient method they are familiar with. Do not get confused with the % sign and 100 multiplied on the right hand side, i.e.
\[x\%=\dfrac{SP-CP}{CP}\] (Wrong)
If one is writing % on the left hand side, then, there is no need to multiply 100 on RHS because both mean the same.
\[x=\dfrac{SP-CP}{CP}\] (Correct)
\[x\%=\dfrac{SP-CP}{CP}\times 100\] (Correct)