Discount
Terms
Marked price (MP)
Marked price or mark up price (MP) is the price which the shopkeeper fixes in anticipation of some discount being asked by customer.
Marked price (M.P.) = C.P. + markup
Discount (D)
Discount means reduction of marked price to sell at a lower rate. It is calculated on the basis of marked price (M.P.)
SP = MP – Discount = MP (1 – Discount%/100)
[Note that (1 – Discount%/100) is the multiplying factor.]
If no discount is given, then
So, SP = MP
Discount percentage
Profit or Loss percentage is always calculated on the cost price. Whereas, Discount percentage is calculated on marked price (or list price).
Discount percent = (Discount / MP) x 100
Finding net profit/loss percentage
The shopkeeper buys at CP and then marks the item up by m% (of CP) to get MP. After that he gives a discount of d% (of MP) to get SP.
So, if a shopkeeper marks the products at m% above the cost price and gives the customer a discount of d%, then
final profit or loss % = m − 𝑑 − $\frac{(m × 𝑑)}{100}$% (successive percentage changes formula)
Q. If a businessman marks up his product by 15% over the cost price and thereafter offers a discount of 20%, then find out his profit/loss percentage.
Explanations :
Let initial C.P. be Rs 100. Then, M.P. = 100 + 15% of 100 = Rs. 115
Now, S.P. = 115 – 20% of 115 = 115 - 23 = Rs. 92
So, loss percentage = (loss/C.P.) × 100 = (8/100) × 100 = 8%
So, if a shopkeeper marks the products at m% above the cost price and gives the customer a discount of d%, then
final profit or loss % = m − 𝑑 − $\frac{(m × 𝑑)}{100}$% = 15 − 20 − $\frac{(15 × 20)}{100}$% = -5 – 3 = -8%
(minus sign denotes that there has been a loss)
In terms of multiplying factors, $MF_{loss/profit}$ = $MF_{mark-up}$ × $MF_{discount}$ = 1.15 × 0.80 = 0.92
So, it means that SP/CP = 0.92
Hence, loss percentage = (1 – 0.92) × 100 = 8%
15% = 3/20. So, if CP = 20, then MP = 20 + 3 = 23
20% = 1/5. So, if MP = 5, then SP = 5 – 1 = 4
But we know MP is 23, so SP = (4/5) × 23
So, if CP = 20, then SP = (4/5) × 23
Therefore, if CP = 100, then SP = (4/5) × 23 × (100/20) = 92
So, loss percentage = 8%
Instead of doing all this, we can shorten our calculation by doing this:
15% = 3/20, so MP/CP = 23/20
20% = 1/5, so SP/MP = 4/5
So, SP/CP = (23/20) × (4/5) = 92/100
Hence, loss percentage = 8%
Q. A shopkeeper gives 30% discount on the clothes he sell, but still manages to make a profit of 5%. What must be the mark up percentage?
Explanations :
Let CP = Rs. 100
As he makes a profit of 5%, so SP = 100 + 5% of 100 = Rs. 105
As 30% discount was given, we can say that 70% is equivalent to Rs. 105
Hence, 100% will be equivalent to 105 × (100/70) = Rs. 150
So, mark-up percentage = (50/100) × 100 = 50%
30% discount = 3/10, so SP/MP = 7/10
5% profit = 1/20, so SP/CP = 21/20
So, MP/CP = (10/7) × (21/20) = 3/2 = 1.5
Hence, mark-up percentage = 50%
Let C.P. = Rs. 100 and the mark up percentage be x%.
Hence, M.P. = Rs. 100 + x
And S.P. = 70% of (100 + x) = 0.70 (100 + x)
As he makes a profit of 5%, his S.P. must be Rs. 105.
So, 0.70 (100 + x) = 105
or 70 + 0.7x = 105
or 0.7x = 35
or x = 50%