In order to maintain the price line, a trader allows a discount of 12 % on the marked price of goods in his ship. However, he still makes a gross profit of 32 % on the cost price. Find the profit percent he would have made on the selling price had he sold at the marked price. A. 28.07 % B. 50 % C. 31.21 % D. 23 % E. 40%
Answers
Given that:
- A trader allows a discount of 12 % on the marked price of goods in his ship.
- He still makes a gross profit of 32 % on the cost price.
To Find:
- The profit percent he would have made on the selling price had he sold at the marked price.
Formula used:
- SP = {CP(100 + P%)}/100
- MP = {100(SP)}/(100 - D%)
- P = SP' - CP
- P'% = {100(P)}/CP %
Where,
- SP = Selling price
- CP = Cost price
- MP = Marked price
- SP' = New selling price
- P% = Profit percent
- D% = Discount percent
- P = Profit
- P'% = New profit percent
Let us assume:
- The cost price of goods be Rs. 100.
Finding selling price:
SP = {CP(100 + P%)}/100
↠ SP = {100(100 + 32)}/100
↠ SP = {100(132)}/100
↠ SP = 132
Finding marked price:
MP = {100(SP)}/(100 - D%)
↠ MP = {100(132)}/(100 - 12)
↠ MP = {13200}/88
↠ MP = 150
If he sold at the marked price.
- SP' = MP = 150
- CP = 100
SP' is greater than CP.
P = SP' - CP
↠ P = 150 - 100
↠ P = 50
Finding new profit percent:
P'% = {100(P)}/CP %
↠ P'% = {100(50)100 %
↠ P'% = 50 %
Hence,
- The profit percent if he sold at the marked price is 50%.
Answer:
Given :-
In order to maintain the price line, a trader allows a discount of 12 % on the marked price of goods in his ship. However, he still makes a gross profit of 32 % on the cost price.
To Find :-
Profit percentage
Solution :-
We know that
SP = (100 + P%)/100 × CP
let the CP be x
SP = (100 + 32)/100 × x
SP = 132x/100
Now
MP = 100/(100 - D%) × SP
MP = 100/(100 - 12) × 132x/100
MP = 132x/88
MP = 1.5x
Now
MP = SP
P = SP - CP
P = 1.5x - x
P = 0.5x
Profit% = Profit/CP × 100
Profit% = 0.5x/x × 100
Profit% = 0.5 × 100
Profit% = 50%