Exercise 13.1
1. A student buys a pen for Rs 90 and sells it for Rs 100. Find his gain and gain percent.
Solution:
Cost price of pen = Rs. 90
Selling price of pen = Rs. 100
Hence,
2. Rekha bought a saree for Rs.1240 and sold it for Rs. 1147. Find her loss and loss percent.
Solution:
As C.P of saree = Rs. 1240
and S.P of saree = Rs. 1147
Loss = CP-SP
= Rs (1240-1147)
Loss = Rs. 93
Loss% = 7.5%
3. A boy buys 9 apples for Rs. 9.60 and sells them at 11 for Rs.12. find his gain or loss percent.
Solution:
4. The cost price of 10 articles is equal to the selling price of 9 articles. Find the profit percentage.
Solution:
Let the cost price of 1 article be Rs. C
Let the selling price of 1 article be Rs. S
Therefore, 10C = 9S
1 C = (9/10)S
So the cost price is less than the selling price.
Profit = S.P – C.P
5. A retailer buys a radio for Rs.225. his overhead expense are Rs15. if he sells the radio for Rs.300, determine the profit percentage.
Solution:
Radio cost = Rs 225
Overhead expenses = Rs 15
Total expenses = Rs. (225 + 15) = Rs.240
S.P = Rs.300
Profit = SP – CP = Rs (300 – 240) = Rs.60Radio cost = Rs 225
Overhead expenses = Rs 15
Total expenses = Rs. (225 + 15) = Rs.240
S.P = Rs.300
Profit = SP – CP = Rs (300 – 240) = Rs.60
= 25%
6. A retailer buys a cooler for Rs.1200 and overhead expenses are on it are Rs.40. if he sells the cooler for Rs.1550, Determine the profit percentage.
Solution:
As Cooler cost = Rs.1200
and Overhead cost = Rs.40
So, Total cost = Rs.(1200+40) = Rs.1240
Now, S.P of the cooler = 1550
Profit = S.P-C.P
= Rs.(1550-1240)
= Rs. 310
7. A dealer buys a wristwatch for Rs 225 and spends Rs 15 on its repairs. If he sells the same for Rs 300, find his profit percent.
Solution:
Cost price of wrist watch = Rs.225
Cost of repairing = Rs.15
Total cost = Rs. 225+15 = Rs.240
Selling price of watch = Rs. 300
Gain = Rs. 300-240 = Rs.60
8. Ramesh bought two boxes for Rs.1300. he sold one box at a profit of 20% and the other at a loss of 12%. If the selling price of both boxes.
Solution:
Let the cost price of the first box be Rs. x
Therefore, the cost of the second box will be Rs.(1300 – x)
Profit on the first box = 20%
Loss on the second box = 12%
The cost price of first box is Rs. 550
Cost price of the second box = Rs. (1300 – 550)
= Rs. 750
The cost prices of the 2 boxes are Rs.550 and Rs.750 respectively.
9. If the selling price of 10 pens is equal to cost price of 14 pens, find the gain percent?
Solution:
Let the cost price of one pen be Rs. C
The selling price be Rs. S
Therefore, 10S = 14C
C = (10/14)S
However, the cost price is less than the selling price.
Profit = 140 – 100
Profit % = 40%
The required profit percentage is 40%.
10. If the selling price of 18 chairs be equal to selling price of 16 chairs, find the gain or loss percent.
Solution:
Cost price of 18 chairs = selling price of 16 chairs
Let cost price of 1 chair = Rs. X
Selling price of 16 chairs =Rs. 18X
11. If the selling price of 18 oranges is equal to the cost price of 16 oranges, find the gain or loss percentage
Solution:
Assume the C.P of one chair be Rs. C
S.P be Rs. S
So, 18C = 16S
But, the C.P of the chair is more than that of S.P.
12. Ravish sold his motorcycle to Vineet at a loss of 28%. Vineet spent Rs.1680 on it’s repairs and sold the motorcycle to Rahul for Rs.35910, thereby making profit of 12.5%, find the cost price of the motorcycle for Ravish.
Solution:
Assume the C.P of the motor cycle for Ravish be Rs. y
And Loss % = 28%
And Ravish paid Rs. 42000 for the motorcycle.
13. By selling a book for Rs.258, a bookseller gains 20%. Find how much should he sell to gain 30%?
Solution:
Aa S.P of the book = Rs. 258
and Gain = 20%
= Rs. 279.50
Hence, the book seller should keep the S.P of the book as Rs. 279.50 to get 30% profit.
14. A defective briefcase costing Rs.800 is being sold at a loss of 8%. If the price is further reduced by 5%, find its selling price?
Solution:
C.P of the briefcase = Rs. 800
Loss = 8%
The selling price of the briefcase is Rs. 699.20
15. By selling 90 ball pens for Rs160 a person loses 20%. How many ball pens should be sold at Rs.96 so as to have a profit of 20%?
Solution:
16. A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs 36.75 less, he would have gained 30%. Find the cost price of the article.
Solution:
17. A dishonest shopkeeper professes to sell pulses at his cost price but uses a false weight of 950 gm for each kilogram. Find his gain percentage.
Solution:
He sells 950 gm pulses and gets grain 50 gm.
If he sells 10 gm of pulses, he will gain:
18. A dealer bought two tables for Rs.3120. he sold one of them at a loss of 15% and the other at a gain of 36%. Then, he found that each table was sold for the same price. Find the cost price of each table.
Solution:
Given that the selling price is same for both the tables.
Let the C.P of 1 table be x
Then the C.P of the other table be = Rs.3120 – x
Loss on the first table = 15%
Therefore, S.P = 85 x 10
= 0.85x
Gain on the second table = 36%
136(3120 – x)
Since both the tables have the same S.P
2.21x = 4243.20
= x= 1920
The cost price of the table is Rs.1920
The cost price of the other table is Rs. (3120 – 1920) = Rs.1200
19. Mariam bought two fans Rs.3605. she sold one of them at a profit of 15% and the other one at a loss of 9 %. If Mariam obtained the same amount for each fan, find the cost price of the each of the fans.
Solution:
It is given that the S.P is same for both of the fans.
Let the C.P of the first fan be Rs. x
Therefore, C.P of the second fan be Rs. (3605 – x)
Profit on the first fan = 15%
Loss on the second fan = 6%
= x = 1592
C.P Of the first fan = Rs. 1592
C.P of the second fan = Rs. (3605-1592)
= Rs. 2012.50
The cost price of the both of the fans are Rs. 1592 and Rs. 2012.50 respectively.
20. Some toffees are bought at a rate of 11 for Rs.10 and the same number at the rate of 9 for Rs.10. if the whole lot is sold at one per toffee, find the gain or loss percent on the whole transaction.
Solution:
Assume the total number of toffees got be Rs. y
Also, y2 at the rate of 11 have got for Rs.10,
As it is given that y toffees will be sold at Re.1 per toffee.
So, the S.P of y toffees = Rs. y(1)
As Cost Price is more than Selling Price, it will be a loss.
So, the Loss= C.P-S.P
Therefore, the total loss on the whole transaction will be 1%
21. A tricycle is sold at a gain of 16%. Had it been sold for Rs.100 more, the gain would have been 20%. Find the C.P of the tricycle.
Solution:
Assume the S.P of the tricycle be Rs. y
and Assume the C.P of the tricycle be Rs. x
As Profit % = 16%
Now we have,
= y = x+0.16x
The put y = 1.6x
= 1.16+100 = x+0.2x
= 1.16+100 = 1.2
= x = 2500
The cost Price of the cycle is 2500
Thus, Cost Price of the tricycle is Rs. 2500.
22. Shabana bought 16 dozens ball pens and sold them at a loss of to S.P of 8 ball pens.
Find:
(i) Her loss percent
(ii) P of 1 dozen ball pens, if she purchased these 16 dozens ball pens for Rs.576
Solution:
(i) Number of pens bought = 16(12) = 192
Assume S.P of 1 pen be Rs. y
Hence, S.P of 192 pens = 192y
Cost Price of 8 pens = Rs. 8y
S.P of 8 pens is equal to the loss of selling 192 pens. (Given)
So, loss= Rs.8y
Cost Price of 192 pens = Rs 576
Now, Loss = C.P –S.P
= 576 y = 576200
= y = 2.88
Hence, loss= RS.23.04
Loss% = 4%
(ii) P of 1 pen = Rs.2.88
hence, S.P of 1 dozen pens = 12y = 12(2.88)
= Rs.34.56
23. The difference between two selling pieces of a shirt at a profit of 4 % and 5% is Rs.6.
Find:
(i) P of the shirt
(ii) The two selling prices of the shirt
Solution:
Assume the C.P of two of the shirts be RS. y
And for one shirt profit = 4%
Now, Profit percent = Rs. 0.04y
and S.P = Rs.1.04y
so, For 2 shirt profit will be = 5%
Profit percentage = Rs. 0.05y
Selling Price = Rs.1.05y
The difference between their profits is Rs.6(Given)
Hence, 1.05y-1.04y = 6
= y = Rs.600
So, C.P = Rs.600
Selling Price of one shirt 1 = Rs.1.04y = Rs. 1.04(600)= Rs. 624
Selling Price of one shirt 2 = Rs.1.05y= Rs. 1.05(600)= Rs. 630
24. Toshiba bought 100 hens for Rs 8000 and sold 20 of these at a gain of 5%. At what gain percent she must sell the remaining hens so as to gain 20% on the whole?
Solution:
gain of 5% on 80 = (1.05×80) = 84 each
or (20×84) = 1680 total
she want a total of 20% gain on 8000 =
(1.2×8000) = 9600 total
she need to make 9600 – 1680 = 7920 total on the last 80 hens.
she originally paid (80×80) = 6400 for those hens.