Question

In a scheme, a pack of three soaps with the MRP Rs.45 is available at Rs.42. If it still gives a profit of 5% to the shopkeeper, then find the cost price of the pack.

Hint:- The selling price is Rs.42 and profit is 5% of the cost price. Selling price is the sum of cost price and the profit. the value of profit is equal to the difference between selling price and cost price. where the selling price is greater than the cost price.

Given , a pack of three soaps with MRP Rs.45 is being sold at Rs.42. The shopkeeper is earning a profit of 5%. We need to find the cost price of the pack.
Let the cost price be Rs. $X$.
Now,
Selling Price(S.P.) = Cost Price(C.P.) + Profitâ€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦.(1)
Profit = $\dfrac{{{\text{Profit percentage}}}}{{100}} \times$C.P. â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦.(2)
Putting the value of profit percentage in above equation we get,
Profit = $\dfrac{5}{{100}} \times$ $X$â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦.(3)
Putting the value of profit in equation (1) , we get
S.P. = $X$ + $\dfrac{5}{{100}} \times$ $X$
42 = $X$ $\left( {1 + \dfrac{5}{{100}}} \right)$
42 = $X$ $\left( {\dfrac{{105}}{{100}}} \right)$
$X$ = $\dfrac{{42 \times 100}}{{105}}$
$X$ = 40
Hence, the cost price of the pack is Rs.40.
Note:- In these types of questions, we need to remember the selling price is not always equal to the MRP. The selling price can have other formulas also in terms of loss.