PAGE NO 13.11:
Question 1:
A student buys a pen for Rs 90 and sells it for Rs 100. Find his gain and gain percent.
ANSWER:
C.P of pen = Rs. 90
S.P of pen = Rs. 100
Gain = SP −CP
Gain = 100−90 = Rs. 10
Gain% =
PAGE NO 13.11:
Question 2:
Rekha bought a saree for Rs 1240 and sold it for Rs 1147. Find her loss and loss percent.
ANSWER:
C.P of saree = Rs. 1240
S.P of saree = Rs. 1147
Loss = CP−SP
Loss = Rs.(1240−1147) = Rs. 93
loss% =
= 7.5%
PAGE NO 13.11:
Question 3:
A boy buys 9 apples for Rs 9.60 and sells them at 11 for Rs 12. Find his gain or loss percent.
ANSWER:
C.P of 9 apples = Rs 9.60
∴ C.P of 1 apple = Rs 9.609 = Rs16/15
S.P of 11 apples = Rs 12
∴ S.P of 1 apple = Rs 12/11
Clearly, S.P of 1 apple >C.P of 1 apple
So, we get profit on selling apples
PAGE NO 13.11:
Question 4:
The cost price of 10 articles is equal to the selling price of 9 articles. Find the profit percent.
ANSWER:
Let the cost price of one article be Rs. C and the selling price be Rs. S
Therefore, 10C = 9S
C = 9/10.S
So, the cost price is less than the selling price.
S.P. =
1000/9 = 100 + Profit
00/9−100 = Profit%
Profit% =
=
Therefore, the required profit percent is
PAGE NO 13.11:
Question 5:
A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. If he sells the radio for Rs 300, determine his profit percent.
ANSWER:
Radio costs = Rs. 225
Overhead expenses = Rs. 15
C.P = Rs. (225 + 15) = Rs. 240
S.P = Rs. 300
Profit = SP−CP
= Rs. (300−240)
= Rs. 60
Profit% = Profit/C.P × 100
= 60/240 × 100 = 25%
PAGE NO 13.11:
Question 6:
A retailer buys a cooler for Rs 1200 and overhead expenses on it are Rs 40. If he sells the cooler for Rs 1550, determine his profit percent.
ANSWER:
Cooler costs = Rs.1200
Overhead expenses = Rs. 40
C.P = Rs. (1200 + 40) = Rs. 1240
S.P = Rs. 1550
Profit = SP−CP
= Rs. (1550−1240)
= Rs. 310
Profit% = Profit/C.P × 100
= 310/1240 × 100
= 25%
PAGE NO 13.11:
Question 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.
ANSWER:
A dealer buys a wrist watch for Rs. 225
Money spent on repairing the watch = Rs. 15
Therefore,C.P = Rs. (225 + 15) = Rs. 240
S.P = Rs. 300
Profit = SP−CP
= Rs. (300−240)
= Rs. 60
Profit% = Profit/C.P × 100
= 60/240 × 100
= 25%
PAGE NO 13.11:
Question 8:
Ramesh bought two box es for Rs 1300. He sold one box at a profit of 20% and the other box at a loss of 12%. If the selling price of both box es is the same, find the cost price of each box .
ANSWER:
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%
SP of the first box = CP
SP = x (120/100)
SP of the first box = Rs.120 x 100 = Rs.6 x 5
SP of the second box = CP
S.P of the second box =
Since S.P of both the box are equal,
150 x = 143000−110 x
260 x = 143000
x = 143000/260
x = 550
Therefore, the cost price of the first box is Rs. 550.
The cost price of the second box will be Rs.(1300−550) = Rs. 750
PAGE NO 13.11:
Question 9:
If the selling price of 10 pens is equal to cost price of 14 pens, find the gain percent.
ANSWER:
Let the cost price of one pen be Rs. C, and the selling price be Rs. S
Therefore, 10S = 14C
C = 10/14.S
However, the cost price is less than the selling price.
S.P. =
1400/10 = 100 + profit%
140−100 = profit%
Profit% = 40 = 40%
Therefore, the required profit percent is 40%.
PAGE NO 13.11:
Question 10:
If the cost price of 18 chairs be equal to selling price of 16 chairs, find the gain or loss percent.
ANSWER:
Let the cost price of one chair be Rs. C, and selling price be Rs. S
Therefore, 18C = 16S
C = 16/18.S
As cost price is less than the selling price,
S.P. =
1800/16 = 100 + profit%
180016−100 = profit%
Profit% =
= 200/16 = 12.5
Therefore, the required profit percent is 12.5%.
PAGE NO 13.11:
Question 11:
If the selling price of 18 oranges is equal to the cost price of 16 oranges, find the loss percent.
ANSWER:
Let the cost price of one orange be Rs. C, and its selling price be Rs. S
Therefore, 16C = 18S
C = 18/16.S
As cost price is more than the selling price,
S.P. =
1600/18 = 100−loss%
Loss% = 100−1600/18
Loss% =
= 200/18 = 100/9
=
Therefore, the loss percent is %.
PAGE NO 13.11:
Question 12:
Ravish sold his motorcycle to Vineet at a loss of 28%. Vineet spent Rs 1680 on its repairs and sold the motor cycle to Rahul for Rs 35910, thereby making a profit of 12.5%, find the cost price of the motor cycle for Ravish.
ANSWER:
Let the cost price of the motorcycle for Ravish be Rs. x .
Loss% = 28%
Therefore, SP = CP
SP = Rs. x (72/100)
Selling price of the motorcycle for Ravish = Cost price of the motorcycle for Vineet
Money spent on repairs = Rs. 1680
Therefore, total cost price of the motorcycle for Vineet = Rs.( x (72/100) + 1680)
Selling price of the motorcycle for Vineet = Rs. 35910
Profit% = 12.5%
SP = CP
⇒ 35910 × 100 × 100 = (72 x + 168000)(112.5)
⇒ 359100000 = 8100 x + 18900000
⇒ 340200000 = 8100 x
⇒ x = Rs. 42000
Therefore, Ravish bought the motorcycle for Rs. 42000
PAGE NO 13.12:
Question 13:
By selling a book for Rs 258, a bookseller gains 20%. For how much should he sell it to gain 30%?
ANSWER:
Selling price of the book = Rs. 258
Gain% = 20%
Since, C.P =
= 25800/120
= Rs. 215
Let the bookseller sells it for Rs. x
So, S.P =
= Rs. 279.50
Therefore, the bookseller must sell the book at Rs 279.50 to make 30% profit.
PAGE NO 13.12:
Question 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.
ANSWER:
C.P of the briefcase = Rs. 800
Loss = 8%
S.P = CP
= 800 × 0.92
= Rs. 736
If the price is further reduced by 5%, the selling price of the briefcase will be
= Rs.(736−736 × 5/100)
= 736 × 0.95
= Rs. 699.20
Thus, the selling price of the briefcase will be Rs 699.20.
PAGE NO 13.12:
Question 15:
By selling 90 ball pens for Rs 160 a person loses 20%. How many ball pens should be sold for Rs 96 so as to have a profit of 20%?
ANSWER:
S.P of 90 ball pens = Rs. 160
Loss = 20%
Therefore, C.P = SP
= Rs. 200
Now,S.P of 90 ball pens = Rs. 96
Profit = 20%
C.P = SP
CP =
= 9600/120
= Rs. 80
Rs. 200 is the C.P of 90 ball pens.
Therefore, Rs. 80 is the C.P of = = 36 ball pens
Thus, 36 ball pens should be sold at Rs. 96 to earn a profit of 20%.
PAGE NO 13.12:
Question 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.
ANSWER:
Let the C.P of the article be Rs. x .
Original S.P = x + 25/100.x
= Rs. 5x/4
If he purchased it at 20% less,C.P = x −20/100.x
= Rs. 4x/5
He sold the article at Rs 36.75 less.
So, the selling price = Rs. 5x/4−36.75
Given that he would have gained 30% selling at that price.
Therefore, gain% =
S.P−C.P = 5x/4−36.75−4 x 5
= 5x/4−4x/5−36.75
−36.75
= 9x/20−36.75
So, gain% =
225 x −18375 = 120 x
105 x = 18375 x
= 18375/105
= 175
So, the cost price of the article is Rs. 175.
PAGE NO 13.12:
Question 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 percent.
ANSWER:
He sells 950gm pulses and gets a gain of 50gm.
If he sells 100gm of pulses, he will gain = 509/50 × 100
= 5000/950
PAGE NO 13.12:
Question 18:
A dealer bought two tables for Rs 3120. He sold one of them at a loss of 15% and 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.
ANSWER:
Given that the selling price is same for both the tables.
Let the C.P of 1 table be Rs. x , then the C.P of the other will be Rs.(3120− x ).
Loss on the first table = 15%
Therefore, S.P = C.P
S.P = 85x/100 = Rs. 0.85 x
Gain on the second table = 36%
Therefore, S.P = C.P
S.P = Rs. 1.36(3120− x )
Since both tables have the same S.P,
So, 0.85 x = 1.36(3120− x )
0.85 x = 4243.20−1.36 x
2.21 x = 4243.20
x = 4243.20/2.21
x = Rs. 1920
So,the cost price of the first table is Rs. 1920.
Cost price of the second table = Rs. ( 3120−1920) = Rs. 1200
PAGE NO 13.12:
Question 19:
Mariam bought two fans for Rs 3605. She sold one at a profit of 15% and the other at a loss of 9%. If Mariam obtained the same amount for each fan, find the cost price of each fan.
ANSWER:
It is given that the S.P is same for both the fans.Let C.P of the first fan be Rs. x
Therefore, C.P of the second fan = Rs. (3605− x )
Profit on the first fan = 15%
Loss on the second fan = 9%
For the first fan,S.P = C.P
For the second fan,S.P = C.P
= (3605− x )(91/100)
Since S.P of both the fans is the same,23x/20 = (3605− x )(91/100)
2300 x = 91(72/100−20 x )2300
x = 6561100−1820 x
4120 x = 6561100
x = Rs.1592.50
Thus, C.P of the first fan is Rs. 1592.50.C.P of the second fan = Rs. (3605−1592.50) = Rs. 2012.50
PAGE NO 13.12:
Question 20:
Some toffees are bought at the 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 rupee per toffee, find the gain or loss percent on the whole transaction.
ANSWER:
Let the total number of toffees bought be x.
Let x/2 toffees at the rate of 11 are bought for Rs.10, and x/2 toffees at the rate of 9 are bought for Rs.10
Total money spent on buying the toffees = (x/2)(10/11) + (x/2)(10/9)
= 200x/198
= 100/99 x
It is given that x toffees are sold at one rupee per toffee.
Therefore, the selling price of x toffees = Rs. x × 1 = Rs. x
As C.P is more than S.P, it will be a loss.
Loss = C.P−S.P
= x/99
Loss% = Loss/C.P × 100
Total loss on the whole transaction would be 1%.
PAGE NO 13.12:
Question 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.
ANSWER:
Let the S.P of the tricycle be Rs. x and C.P be Rs. y Gain% = 16%
S.P = C.P
Then we have, x = y +
x = y + 0.16y
x = 1.16y
When S.P increases by Rs. 100,
we get
⇒ x + 100 = y +
Putting x = 1.6y, we get
⇒ 1.16y + 100 = y + 0.2y
1.16y + 100 = 1.2y
0.04y = 100
y = 100/0.04
= 2500
Thus, C.P of the tricycle is Rs. 2500.
PAGE NO 13.12:
Question 22:
Shabana bought 16 dozen ball bens and sold them at a loss equal to S.P. of 8 ball pens. Find
(i) her loss percent
(ii) S.P. of 1 dozen ball pens, if she purchased these 16 dozen ball pens for Rs 576.
ANSWER:
(i) Number of pens bought = 16 × 12 = 192
Let the S.P of one pen be Rs. x .
Therefore, S.P of 192 pens = Rs. 192 x S.P of 8 pens = Rs. 8 x
It is given that S.P of 8 pens is equal to the loss on selling 192 pens.
Therefore, loss = Rs. 8 x C.P of 192 pens = Rs. 576
So, loss = C.P−S.P
8 x = 576−192 x
200 x = 576
x = 576/200 = 2.88
Therefore, loss = 8(2.88) = Rs. 23.04
= 4%
(ii) S.P of 1 pen = Rs. 2.88
Therefore, S.P of 1 dozen pens = 12x
= 12 × 2.88
= Rs. 34.56
PAGE NO 13.12:
Question 23:
The difference between two selling prices of a shirt at profits of 4% and 5% is Rs 6. Find
(i) C.P. of the shirt
(ii) the two selling prices of the shirt
ANSWER:
Let the C.P of both the shirts be Rs. x .C.P = Rs. x
For shirt 1:
Profit is 4%:
Profit% = Profit/CP × 100
Profit = 4/100 × C.P
= Rs. 0.04 x S.P
= C.P + Profit = x + 0.04
x = Rs. 1.04 x
For shirt 2:Profit = 5%:
C.P = Rs. x
Profit = 5/100 × C.P = Rs. 0.05 x
S.P = C.P + Profit = x + 0.05
x = Rs. 1.05 x
It is given that the difference between their profits is Rs. 6
So, 1.05 x −1.04 x = 6
0.01 x = 6
x = Rs. 600
Thus, C.P = Rs. 600
S.P of shirt 1 = Rs. 1.04 x
= Rs. 1.04 × 600
= Rs. 624
S.P of shirt 2 = Rs.1.05 x
= Rs.1.05 × 600
= Rs. 630.
PAGE NO 13.12:
Question 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?
ANSWER:
C.P of 100 hens = Rs. 8000
Cost of one hen = 8000/100 = Rs. 80
C.P of 20 hens = Rs.( 80 × 20) = Rs. 1600
Gain% = 5%
S.P = C.P
S.P = 1600 × 105/100 = Rs. 1680
C.P of 80 hens = Rs.(80 × 80) = Rs.6400
Gain on 80 hens = S.P of 80 hens−C.P of 80 hens
Gain on 100 hens = Gain on 80 hens + Gain on 20 hens
Gain on 100 hens = Rs.(80 + S.P of 80 hens − 6400)
Gain% on 100 hens =
1600 = 80 + S.P of 80 hens − 6400
S.P of 80 hens = Rs.( 1600 + 6400−80)S.P of 80 hens = Rs. 7920
Gain on 80 hens = S.P of 80 hens −C.P of 80 hens = Rs.(7920−6400) = Rs.1520
Gain% on 80 hens = Gain on 80 hens
C.P of 80 hens = 23.75%
Therefore, Toshiba gained 23.75% on 80 hens.
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