Question 14: A shopkeeper marks his goods in such a way that after allowing a discount of 25% on the marked price, he still makes a profit of 50%. Find the ratio of the C.P. to the M.P.
Solution:
Here, Discount% given to customer = 25%
Profit% earned by shopkeeper = 50%
Using Formula, C.P = (S.P * 100)/(100 + Profit%)
Hence, C.P = (S.P * 100)/(100 + 50)
= (S.P * 100)/150
= (2 * S.P)/3
Using Formula, M.P = (S.P * 100)/(100 – Discount%)
Hence, M.P = (SP * 100)/(100 – 25)
= (S.P * 100)/75
= (4 * S.P)/3
Ratio of C.P to M.P = ((2 * S.P)/3)/ ((4 * S.P)/3)
= 1:2
Question 15: A cycle dealer offers a discount of 10% and still makes a profit of 26%. What is the actual cost to him of a cycle whose marked price is Rs 840?
Solution:
Here, M.P of the cycle = Rs 840
Discount% given to customer = 10%
Profit% earned by cycle dealer = 26%
To find C.P of cycle.
Using Formula, S.P = (M.P * (100 – Discount%))/100
Hence, S.P of goods = Rs (840 * (100 – 10))/100
= Rs (840 * 90)/100
= Rs 756
Using Formula, C.P = (S.P * 100)/(100 + Profit%)
Hence, C.P of goods = Rs (756 * 100)/(100 + 26)
= Rs (756 * 100)/126
= Rs 600
Question 16: A shopkeeper allows 23% commission on his advertised price and still makes a profit of 10%. If he gains Rs 56 on one item, find the advertised price.
Solution:
Here, Commission% = 23% (It is same as discount percentage)
Profit% of shopkeeper = 10%
Profit of shopkeeper = Rs 56
Using Formula, Profit% = (Profit * 100)/C.P
Hence, C.P = (Profit * 100)/Profit%
Here C.P = Rs(56 * 100)/10
= Rs 560
Using Formula, S.P = (C.P * (100 + Profit%))/100
Hence, S.P = Rs (560 * (100 + 10))/100
= Rs (560 * 110)/100
= Rs 616
Using Formula, M.P = (S.P * 100)/(100 – Discount%)
Hence, M.P = Rs (616 * 100)/(100 – 23)
= Rs 800
Question 17: A shopkeeper marks his goods at 40% above the cost price but allows a discount of 5% for cash payment to his customers. What actual profit does he make, if he receives Rs 1064 after paying the discount?
Solution:
Here, Mark up percentage = 40%
Discount% = 5%
S.P of the goods = Rs 1064
Let the C.P of the goods be Rs y.
Then the M.P of the goods would be Rs 1.40y.
Using Formula, S.P = (M.P * (100 – Discount%))/100
Hence, S.P of the goods = Rs (1.40y * (100 – 5))/100
Rs 1064 = Rs (1.40y * 95)/100
or y = Rs (1064 * 100)/(1.40 * 95)
= Rs106400/133
= Rs 800
Now Using Formula, Profit = (S.P – C.P)
We have, Profit = Rs (1064 – 800)
= Rs 264
Question 18: A publisher gives 32% discount on the printed price of a book to booksellers. What does a bookseller pay for a book whose printed price is Rs 275?
Solution:
Here, Discount% given by book publisher = 32%
Printed price = Rs 275
Using Formula, S.P = (M.P * (100 – Discount%))/100
Hence, S.P of publisher or cost price of bookseller = Rs (275 * (100 – 32))/100
= Rs (275 * 68)/100
= Rs 187
Question 19: After allowing a discount of 20% on the marked price of a lamp, a trader loses 10%. By what percentage is the marked price above the cost price ?
Solution:
Here, Discount% on lamp = 20%
Loss% on lamp = 10%
Let C.P be x.
Then S.P would be (9x)/10.
Using Formula, M.P = (S.P * 100)/(100 – Discount%)
Hence, M.P = (((9x)/10) * 100))/(100 – 20)
= (9x * 10)/80
= (9x)/8
Mark up price = M.P – C.P
= (((9x) /8) – x)
= x/8
Mark up % = ((Mark up price * 100) / C.P)%
= ((x/8) * 100)/ x%
= 12.50%
Question 20: The list price of a table fan is Rs 480 and it and is available to a retailer at 25% discount. For how much should a retailer sell it to gain 15%?
Solution:
Here, List price of a table fan = Rs 480
Discount% = 25%
Profit% = 15%
To find S.P
C.P of retailer = (List price * (100 – Discount%))/100
= Rs (480 * (100 – 25))/100
= Rs (480 * 75)/100
= Rs 360
Using Formula, S.P = (C.P * (100 + Profit%))/100
Hence, S.P of the retailer = Rs (360 * (100 + 15))/100
= Rs (360 * 115)/100
= Rs 414
Question 21: A cycle merchant allows 20% discount on the marked price of the cycles and still makes a profit of 20%. If he gains Rs 360 over the sale of one cycle, find the marked price of the cycle. (in Rs.)
Solution:
Here, Discount% on cycle = 20%
Profit% on cycles = 20%
Profit on cycles = Rs 360
Using Formula, Profit% = (Profit * 100)/C.P
Hence, C.P = (Profit * 100)/Profit%
Here C.P of cycles = Rs(360 * 100)/20
= Rs 1800
Using Formula, S.P = (C.P * (100 + Profit%))/100
Hence, S.P of cycles = Rs (1800 * (100 + 120))/100
= Rs (1800 * 120)/100
= Rs 2160
Using Formula, M.P of cycles = (S.P * 100)/(100 – Discount%)
Hence, M.P = Rs (2160 * 100)/(100 – 20)
= Rs 2700
Question 22: Jyoti and Meena run a ready-made garment shop. They mark the garments at such a price that even after allowing a discount of 12.5%, they make a profit of 10%. Find the marked price of a suit which costs them Rs 1470.
Solution:
Here, C.P of the garment = Rs 1470
Discount% = 12.5%
Profit% earned by Jyoti and Meera = 10%
To find M.P of the article.
Using Formula, S.P = (C.P*(100+Profit%))/100
Hence, S.P of the article = Rs (1470 * (100 + 10))/100
= Rs (1470 * 110)/100
= Rs 16170
Using Formula, M.P = (S.P * 100)/(100 – Discount%)
Hence, M.P of the article = Rs (16170 * 100)/(100 – 12.5)
= Rs (16170 * 100)/87.5
= Rs 1848
Question 23: Jasmine allows 4% discount on the marked price of her goods and still earns a profit of 20%. What is the cost price of a shirt for her marked at Rs 850?
Solution:
Here, M.P of the goods = Rs 850
Discount% given to customer = 4%
Profit% earned by jasmine = 20%
To find C.P of goods.
Using Formula, S.P = (M.P * (100 – Discount%))/100
Hence, S.P of goods = Rs (850 * (100 – 4))/100
= Rs (850 * 96)/100
= Rs 816
Using Formula, C.P = (S.P * 100)/(100 + Profit%)
Hence, C.P of goods = Rs (816 * 100)/(100 + 20)
= Rs (816 * 100)/120
= Rs 680
Question 24: A shopkeeper offers 10% off-season discount to the customers and still makes a profit of 26%. What is the cost price for the shopkeeper on a pair of shoes marked at Rs 1120?
Solution:
Here, M.P of the shoes = Rs 1120
Discount% given to customer =10%
Profit% earned by shopKeeper = 26%
To find C.P of shoes.
Using Formula, S.P = (M.P * (100 – Discount%))/100
Hence, S.P of goods = Rs (1120 * (100 – 10))/100
= Rs (1120 * 90)/100
= Rs 1008
Using Formula, C.P = (S.P * 100)/(100 + Profit%)
Hence, C.P of goods = Rs (1008 * 100)/(100 + 26)
= Rs (1008 * 100)/126
= Rs 800
Question 25: A lady shopkeeper allows her customers 10% discount on the marked price of the goods and still gets a profit of 25% what is the cost price of a fan for her marked at Rs 1250?
Solution:
Here, M.P of the fan = Rs 1250
Discount% given to customer =10%
Profit% earned by shopKeeper = 25%
To find C.P of shoes.
Using Formula, S.P = (M.P * (100 – Discount%))/100
Hence, S.P of fan = Rs (1250 * (100 – 10))/100
= Rs (1250 * 90)/100
= Rs 1125
Using Formula, C.P = (S.P * 100)/(100 + Profit%)
Hence, C.P of fan = Rs (1125 * 100)/(100 + 25)
= Rs (1125 * 100)/125)
= Rs 900