Question

Ramji sold an article at a loss of 8 percent. Had she bought it at 10% less and sold for Rs72 more; she would have gained 20%. Find the cost price of the article.
A) 400
B) 450
C) 500
D) 550

Answer 1

Hint- In this particular type of question we need to assume the CP as 100 and use the loss percentage to find the SP. After this we have to find the SP of the article if the CP is 10% less. With both these results we need to compare them to get the desired result.

Complete step-by-step answer:
Let the CP be Rs 100
Loss=8%
$\begin{gathered}
  SP = CP \times \dfrac{{100 - Loss}}{{100}} \\
   \Rightarrow SP = 100 \times \dfrac{{100 - 8}}{{100}} = Rs92 \\
\end{gathered} $
Now, if she had bought it for 10% less
$CP = 100 - 100 \times \dfrac{{10}}{{100}} = Rs90$
Gain=20%
$SP = CP \times \dfrac{{\left( {100 + P} \right)}}{{100}} = \dfrac{{90 \times 120}}{{100}} = Rs108$
Now, we can see that the difference in both SP’s on assumed CP (Rs100) = 108−92 = Rs16
Actual S.P difference has to be Rs72 as given in the question,
So if CP = 100 then difference = 16
Let if difference= 72 then CP = x
$x = 72 \times \dfrac{{100}}{{16}} = Rs450$
So the cost price is Rs 450 and option (B) is correct.

Note- Remember to recall the formula of selling price and cost price while solving such questions. Note that these types of questions can also be done by expressing the CP as x and then following the similar steps.