Q 9 and 10

Question 9

Question: A trader allows a discount of 15% on the written price. How much above the cost price must he mark his goods to make a profit of 19%?

Step 1: Assume the cost price (C.P.) is ₹100.

Required profit = 19% of ₹100

Profit = ₹19

Therefore, selling price (S.P.) = ₹100 + ₹19 = ₹119

Step 2: Calculate the marked price (M.P.).

Discount = 15% of M.P.

Therefore, S.P. = 85% of M.P.

\(\displaystyle 119=\frac{85}{100}\times\text{M.P.}\)

Hence,

\(\displaystyle \text{M.P.}=\frac{119\times100}{85}=\text{₹}140\)

Step 3: Calculate how much above the cost price the goods are marked.

Excess over C.P. = M.P. − C.P.

= ₹140 − ₹100 = ₹40

Percentage above C.P.:

\(\displaystyle \frac{40}{100}\times100=\boxed{40%}\)

Answer: The goods must be marked 40% above the cost price.

Question 10

Question: A shopkeeper allows 23% commission on his advertised price and still makes a profit of 10%. If he gains ₹56 on one item, find his advertised price.

Step 1: Find the cost price (C.P.).

Profit = ₹56

Profit percentage = 10%

We know that:

\(\displaystyle \text{Profit%}=\frac{\text{Profit}}{\text{C.P.}}\times100\)

Therefore,

\(\displaystyle 10=\frac{56}{\text{C.P.}}\times100\)

\(\displaystyle \text{C.P.}=\frac{56\times100}{10}=\text{₹}560\)

Step 2: Find the selling price (S.P.).

S.P. = C.P. + Profit

= ₹560 + ₹56 = ₹616

Step 3: Find the advertised price (A.P.).

Commission = 23% of advertised price.

Therefore, the selling price received after commission is 77% of the advertised price.

\(\displaystyle 616=\frac{77}{100}\times\text{A.P.}\)

Hence,

\(\displaystyle \text{A.P.}=\frac{616\times100}{77}=\text{₹}800\)

Answer: The advertised price is ₹800.

Remember: Profit percentage is calculated on the cost price, while discount and commission are calculated on the marked or advertised price, respectively.

© abhishek.io.in