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Brilliant’s Composite Mathematics Class 6 Solutions Chapter 9 Percentage Profit and Loss Simple Interest
Welcome to NCTB Solutions. Here with this post we are going to help 6th class students for the Solutions of Brilliant’s Composite Mathematics Class 6 Math Book, Chapter 9, Percentage Profit and Loss Simple Interest. Here students can easily find step by step solutions of all the problems for Percentage Profit and Loss Simple Interest, Exercise 9.1, 9.2, 9.3 and 9.4 Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily.
Percentage Profit and Loss Simple Interest Exercise 9.1 Solution
Question no – (1)
Solution :
(i) 29/100
= (29/100 × 100)
= 29%
(ii) 7/8
= (7/8 × 100 )
= 175/2
= 87.5 %
(iii) 3/7
= (3/7 × 100 )
= 300/7
= 42.857% (approx.)
(iv) 11/20
= 11/20 × 100
= 55%
(v) 17/400
= 17/400 × 100
= 17/4
= 4.25 %
(vi) 1 2/5
= (7/5 × 100)
= 140%
Question no – (2)
Solution :
(i) 0.7
= (7/10 × 100)%= 70%
(ii) 0.23
= (23/ 100 × 100)%
= 2.3%
(iii) 0.35
= (35/100 × 100)%
= 35%
(iv) 0.06
= (6/100 × 100) %
= 6%
(v) 3.05
= (305/100 × 100)%
= 305%
(vi) 0.003
= (3/100 × 100)%
= 0.3%
Question no – (3)
Solution :
(i) Given, 27 %
= 27/100
= 27 : 100
Thus, 27% as ratio in the simplest form is 27 : 100
(ii) 12 1/2 %
∴ 25/2%
= 25/2 × 100
= 1/8
= 1 : 8
Hence, 12 1/2% as ratio in the simplest form is 1 : 8
(iii) 120%
= 120/100
= 6/5
= 6 : 5
Thus, 120% as ratio in the simplest form is 6 : 5
(iv) 6 1/4 %
= 25/4 %
= 25/4 × 100= 1/16
= 1 : 16
Hence, 6 1/4% as ratio in the simplest form is 1 : 16
(v) 0.005%
= 0.05/20000000
= 1/2000
= 1 : 2000
Hence, 0.005% as ratio in the simplest form is 1 : 2000
(vi) 145%
= 145/100
= 29/20
= 29 : 20
Hence, 145% as ratio in the simplest form is 29 : 20
(vii) 3.5%
= 3.5/100 × 10
= 7/200
= 7 : 200
Thus, 3.5% as ratio in the simplest form is 7 : 200
(viii) 0.65 %
= 0.65 / 100 × 100
= 13 : 2000
Therefore, 0.65% as ratio in the simplest form is 13 : 2000
(ix) 0.852%
= 0.852 /100 × 100
= 213/25000
= 213 : 25000
So, 0.852% as ratio in the simplest form is 213 : 25000
(x) 13 1/3 %
= 40/3 × 100
= 2/15
= 2 : 15
Thus, 13 1/3% as ratio in the simplest form is 2 : 15
Question no – (4)
Solution :
(i) 35%
= 35/100
= 7/20
Thus, 35% as fraction in the simplest form is 7/20
(ii) 125 %
= 125/100
= 5/4
Hence, 125% as fraction in the simplest form is 5/4
(iii) 0.25 %
= 0.25 / 100 × 100
= 1/400
Therefore, 0.25% as fraction in the simplest form is 1/400
(iv) 13 1/3 %
= 40 /3 × 100
= 2/15
Hence, 13 1/3% as fraction in the simplest form is 2/15
(v) 0.75%
= 0.75 / 100 × 100
= 3/400
So, 0.75% as fraction in the simplest form is 3/400
Question no – (5)
Solution :
(i) 3 : 7
= (3×7/100)%
= 300/7%
= 42 6/7%
(ii) 2 : 3
= (2/3 × 100)%
= 200/3%
= 66 2/3%
(iii) 135 : 305
= (135/305 × 100)%
= 2700/61
= 44 16/61 %
(iv) 13 : 25
= (13/25 × 100)%
= 52%
(v) 7 : 5
=(7/5 × 100)
= 140%
Question no – (6)
Solution :
(i) 65 %
= 65/100
=0.65
(ii) 9%
= 9/100
= 0.09
(iii) 5.7%
= 5.7/100
= 0.057
(iv) 13.34 %
= 1334 / 100 × 100
= 0.1334
(v) 0.05 %
= 0.05/ 100 × 100
= 0.0005
(vi) 1/4%
= 1/4 × 1/100
= 1/400
= 0.0025
Question no – (7)
Solution :
(i) 350%
= 350/100
= 7/2
= 3 1/2 (mixed number)
(ii) 150 %
= 150/100
= 3/2
= 1 1/2 (mixed number)
(iii) 126 %
= 126/100
= 63/50
=1 50/13 (mixed number)
(iv) 200%
= 200/100
= 2 (whole number)
Question no – (8)
Solution :
(i) 25% off Rs 160
Now, 25/100 × 160
= 40
Thus, the value 25% off on Rs 160 is Rs. 40
(ii) 70% of 125 kg
Now, 70/100 × 125
= 175/2
= 87.5 kg
Thus, the value 70% of 125 kg is 87.5 kg
(iii) 60% of 550 kg
Now,
= 60/100 × 550
= 330 kg
Thus, the value 60% of 550 kg is 330 kg.
(iv) 2 1/2% of 70
Now, 2 1/2 %
= 5/2 × 100 × 70
= 7/4
= 1.75
Thus, the value 2 1/2% of 70 is 1.75
(v) 135% of Rs 80
Now, 135% of Rs 80
= 135/100 × 80
= 108
Thus, the value 135% of Rs 80 is Rs. 108.
(vi) 166 2/3% of 3 metres
Now, 166 2/3%
= 500/3 × 100 × 3
= 5 metres
Thus, the value 166 2/3% of 3 metres is 5 metres.
(vii) 12 1/2% of Rs 130.80
Now, 12 1/2 %
= 25/20 × 100 × 130.8/10
= 327/20
= 16 7/20
= 16.35
Thus, the value 12 1/2% of Rs 130.80 is Rs. 16.35
Question no – (9)
Solution :
(i) Rs 15 of Rs 165
Now, = 15 : 165
= 15/165 × 100
= 100/11
= 9 1/11%
So, Rs 15 of Rs 165 is 9 1/11%
(ii) 36 minutes of 2 hours
Now, 2 hours
= 2 × 60 min (∵ 1 hour = 60 min)
= 120 min
= 36 : 120
= 36/120 × 100
= 30%
Thus, 36 minutes of 2 hours is 30%
(iii) 25 paise of Rs 6
Now, 6 rupees = 600 paise (∵ 1 rupees = 100 paise)
= 25 : 600
= 25/600 × 100
= 25/6
= 4 1/6 %
Thus, 25 paise of Rs 6 is 4 1/6 %
(iv) 125 meters of 3 km
Now, 3 km = 3000 m (∵ 1 km = 1000 metre)
= 125 : 3000
= 125 /3000 × 100
= 25/6
= 4 1/6 %
Hence, 125 meters of 3 km is 4 1/6 %
(v) 0.5 of 4
Now, 0.5 : 4
= 0.5 / 40 × 100
= 50/4
= 12 2/4
= 12 1/2 %
Hence, 0.5 of 4 is 12 1/2 %
(vi) 16 hours of 3 days
Now, = 3 × 24 (∵ 1 day = 24 hours)
= 72 hours
∴ 16 : 72
= 16/12 × 100
= 200/9
= 22 2/9 %
Hence, 16 hours of 3 days is 22 2/9%
Question no – (10)
Solution :
(i) percent of 36 is 9
= 9 : 36
= 9/36 × 100
= 25%
Thus, 25% percent of 36 is 9
(ii) 750 meters is 125 meters
= 125 : 750
= 125/750 × 100
= 50/3
= 16 2/3%
Thus, 16 2/3% percent of 750 meters is 125 meters.
(iii) Rs 55 is Rs 10
= 10 : 55
= 10/55 × 100
= 200/11
= 18 2/11 %
Hence, 18 2/11% percent of Rs 55 is Rs 10
(iv) 5 kg
= 5000 gm (∵ 1 kg = 1000 gms)
= 35 : 5000
= 35/5000 × 100
= 7/10 %
Thus, 7/10% percent of 5 kg is 35 gm
(v) 50 liters is 30 liters
= 30 : 50
= 30/50 × 100
= 60%
Hence, 60% percent of 50 liters is 30 liters.
(vi) 15 kg
= 15000 gm (∵ 1 kg = 1000 gms)
= 1 kg 250 gm
= 1250 gm
∴ 1250 : 15000
= 1250 / 15000 × 100
= 05/3
= 8 1/3 %
Thus, 8 1/3% percent of 15 kg is 1 kg 250 gms.
Question no – (11)
Solution :
Let the quantity be = x
= x × 25/2 × 100
= x = 65 × 8
= 520 kg
Therefore, the quantity will be 520 kg.
Question no – (12)
Solution :
Let the number be x
= x × 13 1/3%
= x × 40/3 × 100 = 18
= x = 18 × 3 × 100/40
= 135
Thus, the required number will be 135
Question no – (13)
Solution :
Given, 25 is 3.5 kg
= 35/250 × 100
= 14%
Thus, 14% per cent of 25 is 3.5 kg
Question no – (14)
Solution :
Let the number be = x
= x × 12 % = 18
= x × 12/100 = 18
= x = 18 × 100/12
= 150
Hence, the required number is 150
Percentage Profit and Loss Simple Interest Exercise 9.2 Solution
Question no – (1)
Solution :
First, Increased value,
= (300 – 250)
= 50
Original value = 250
Now, Percentage = Increased value/original value × 100 %
= 50/250 × 100
= 20%
Therefore, the percentage increase in the rent is 20%
Question no – (2)
Solution :
First, Rises value,
= ( 5.40 – 4 )
= 1.40
Original value = 4
Now, Percentage,
= 1.40/40 × 100
= 35%
Thus, 35% rise in the price of the milk.
Question no – (3)
Solution :
% of marks of English,
= 60/80 × 100
= 75%
% of marks of math,
= 80/90 × 100
= 800/9
= 88.88 %
% of marks of Hindi,
= 33/40 × 100
= 825/10
= 82.5 %
∴ In mathematics his percentage of marks is best
Question no – (4)
Solution :
First, petrol left in tin after leakage,
= (20 – 1.50) litres
= 18.50 litres
Now, percentage
= 18.50/20 × 100
= 92.50%
Therefore, 92.50% petrol is still present in the tin.
Question no – (5)
Solution :
First we find Left area,
= 600 – 450
= 150 sq. metres
∴ Percent to be left without construction,
= 150/600 × 100
= 25%
Thus, 25% percent is to be left without construction.
Question no – (6)
Solution :
12 eggs are 10 rupees
= 6 eggs are 10/2
= 5 rupees
∴ Lost of 4 dozens eggs,
= 4 ×10
= 40 rupees
Loss 5 rupees,
Left = 40 – 5
= 35
∴ Percentage,
= 5/40 × 100
= 25/2
=12.5 %
Thus, 12.5% of his money went waste.
Question no – (7)
Solution :
First, Saving,
= 1/3 × 1500
= 500 Rs
Now, Balance amount,
= 1500 – 500
= 1000 Rs
∴ Amount spend on food and house rent,
= 70% of 1000
= 70/100 × 1000
= 700 Rs
Thus, his spending on food and on house rent is 700 Rs
Question no – (8)
Solution :
First, number of girls,
= (40 – 15)
= 25
∴ Percentage of number of girls,
= 25/10 × 100
= 625/10
= 62.5%
Thus, 62.5% of the class are girls.
Question no – (9)
Solution :
In the given question,
A man spend 65% of his income.
∴ He saves,
= (100 – 65)%
= 35%
Thus, the man save 35% of his income.
Question no – (10)
Solution :
% of mark in Hindi,
= 65/90 × 100
= 650/9
= 72.22%
% of mark in Math,
= 33/40 × 100
= 828/10
= 82.5%
∴ In mathematics his marks is better.
Question no – (11)
Solution :
In the given question,
Amit secures = 84% in English.
The maximum marks in the subject are = 150
∴ The marks secured in English,
= 150 × 80/100
= 126
Therefore, He secured in English 126 marks.
Question no – (12)
Solution :
Given, Synthetic : cotton = 3 : 4
∴ Cotton in the fabric = 4/7
Now, Percentage,
= 4/7 × 100
= 400/7
= 57 1/7%
Thus, 57 1/7% of cotton fibre is there in the fabric.
Question no – (13)
Solution :
Increased number of students,
= 118/100 × 1600
= 18888
∴ Total increased,
= (1888 – 1600)
= 288
Thus, the total increase in enrollment during that year is 288
Question no – (14)
Solution :
From the question we know,
55% of the population of a town are males.
The total population of the town is = 64100,
Total number of males in the town,
= 64100 × 55/100
= 35255
∴ Number of females,
= (64100 – 35255)
= 28845
So, number females in the town is 28845
Question no – (15)
Solution :
Number of apple trees,
= 50/3 × 100 × 240
= 40
∴ Number of other types of trees,
= 240 – 40
= 200
Thus, the number of other type of trees are 200
Question no – (16)
Solution :
Anshul total travelled,
= 50 + 150
= 200
Percentage of travelled by car,
= 50/200 × 100
= 25%
Percentage of travelled by train,
= 150/200 × 100
= 75%
Question no – (17)
Solution :
According to the question,
A school contributed Rs 3000 for the relief of flood victims.
15% of the amount was contributed by the Anshul alone.
∴ Anshul alone contribute,
= 3000 × 15/100
= 450 Rs.
Hence, Anshul alone contribute Rs. 450
Question no – (18)
Solution :
First we find pass marks,
= 190 + 35
= 225
Now, maximum marks,
= 100/36 × 225
= 625 marks
Question no – (20)
Solution :
Let his income = x
∴ Spending,
= x × 85/100
= 854/100
∴ Reminder,
= x – 854/100
= 100x – 854 / 100
= 15x/100
∴ 10% 9n charity,
= 15x/100 × 10/100
= 15x/1000
Now,
= 15x/100 – 15x/1000
= 607.50
= x = (150 – 15/1000)
= 6075/10
= x = 6075/10 × 1000/135
= 4500
Therefore, His income Rs 4500
Question no – (21)
Solution :
In the question,
The approximate population in 1971 was 5480 lakhs
The approximate population in 1981 was 6850 lakhs
∴ Increase value,
= ( 6850 – 5480 )
= 1370 lakhs
∴ Increase percent,
= 1370/5480 × 100
= 25%
Percentage Profit and Loss Simple Interest Exercise 9.3 Solution
Question no – (1)
Solution :
(i) Cost Price = Rs 50
Selling Price = Rs 90
Gain = (90 – 50)
= 40
∴ Gain% = Gain/CP × 100
= 40/50 × 100
= 80%
Thus, gain percent is 80%
(ii) Cost Price = Rs 560
Selling Price = Rs 630
Gain = (630 – 560) = 70
Gain% = Gain/CP × 100
= 70/560 × 100
= 25/2
= 12 1/2%
Thus, gain percent is 12 1/2%
(iii) Cost Price = Rs 300
Selling Price = Rs 315
∴ Gain
= (315 – 300)
= 15
Now, Gain percent,
= Gain/CP × 100
= 15/300 × 100
= 5%
Thus, gain percent is 5%
(iv) Cost Price = Rs 20.25
Selling Price = Rs 22.28
∴ Gain,
= (22.28 – 20.25)
= 2.03
Now, Gain% = Gain/CP × 100
= 2.03/20.25 × 100
= 812/81
= 10.02%
Thus, gain percent is 10.02%
Question no – (2)
Solution :
(i) Cost Price = Rs 400
Selling Price = Rs 380
∴ Loss = 400 – 380 = 20
Now the Loss% = Loss/CP × 100
= 20/400 × 100
= 5%
Thus, gain percent is 5%
(ii) Cost Price = Rs 112.75
Selling Price = Rs 107
Loss
= (112.75 – 107)
= 5.75
∴ Loss% = Loss/CP × 100
= 5.75/112.75 × 100
= 2300/451
= 5 45/451%
Thus, loss percent is 5 45/451%
(iii) Cost Price = Rs 350
Selling Price = Rs 280
∴ Loss = (350 – 280)
= 70 Rs
Now the Loss%
= Loss/CP × 100
= 70/350 × 100
= 20%
Thus, loss percent is 20%
(iv) Cost Price = Rs 450
Selling Price = Rs 360
∴ Loss = (450 – 360)
= 90 Rs
Now, the Loss% = Loss/CP × 100
= 90/450 × 100
= 20%
Thus, loss percent is 20%
Question no – (3)
Solution :
In the given question,
Cost Price = 5000
Gain% = 10%
∴ Total gain%,
= 5000 × 10/100
= 500
Therefore, the Selling Price,
= 5000 + 500
= 5500
Hence, the selling price of the TV is Rs 5500
Question no – (4)
Solution :
As we know, CP = SP + Loss
= 20 + 5
= 25 Rs.
∴ Loss percent (%)
= 5/25 × 100
= 20%
Thus, the loss percent will be 20%
Question no – (5)
Solution :
According to the question,
5 eggs = 6 Rs.
1 eggs = 6/5 Rs.
and
8 eggs = 12 Rs.
1 eggs = 12/8 = 3/2 Rs.
Now,
∴ 6/5 = 6 × 2/5 × 2 = 12/10
∴ 3/2 = 3 × 5/2 × 5 = 15/10
Profit,
= 15/10 – 12/ 10
= 15 – 12 / 10
= 3/10
Profit%
= 3/10 / 6/5 × 100
= (3/10) / (6/65) × 100
= 25%
Question no – (6)
Solution :
First, the gain,
= (1820 – 1680)
= 140 Rs
Now, the gain%,
= 140/1680 × 100
= 25/3
= 8 1/3%
Therefore, the gain percent is 8 1/3%
Question no – (7)
Solution :
Given, total bought price,
= 2465 + 35
= 2500
First we find gain,
= 16/100 × 2500
= 400
∴ Selling Price,
= 2500 + 400
= 2900
Therefore, selling price of the TV set will be Rs 2900.
Question no – (8)
Solution :
Cost Price,
= 10.80 × 4
= 43.20 Rs
Selling Price,
= ( 48 × .80 )
= 38.40 Rs
Now the loss,
= 43.20 – 38.40
= 4.80 Rs
Therefore loss percent(%)
= ( 4.80/43.20 × 100) %
= 100/9
= 11 1/9%
Hence, his loss percent is 11 1/9%
Question no – (9)
Solution :
(i) C.P = Rs 148
Profit = RS 10%
Total profit,
= 148 × 10/100
= 14.8
∴ Selling Price,
= (148 + 14.8)
= 162.8 Rs.
Hence, the Selling Price will be 162.8 Rs.
(ii) C.P = Rs 467
Profit = Rs 14%
Total profit,
= 467 × 14/100
= 6538/100
= 65.38
∴ Selling Price,
= (467 + 65.38)
= 532.38 Rs.
Hence, the Selling Price will be 532.38 Rs.
(iii) C.P = Rs 987
loss = 5 1/2%
Total loss,
= 987 × (11/2)/100
= 987 × 11/2 × 1/100
= 10857/200
= 54.28
∴ Selling Price,
= (987 – 54.28)
= 932.72 Rs
Hence, the Selling Price will be 932.72 Rs.
(iv) C.P = Rs 689.20
Loss = 9%
Total loss,
= 689/100 × 9/100
= 62028/1000
= 62.28
∴ Selling Price,
= 689.200 – 62.028
= 627.172 Rs
Hence, the Selling Price will be 627.172 Rs
(v) C.P = Rs 489.46
Profit = 48 1/33%
Total Profit
= 489.46/100 × 1585/33 × 100
= 9079483/33000
= 275.13
∴ Selling Price,
= (489.46 + 275.13
= 764 .59 Rs
Hence, the Selling Price will be 764 .59 Rs
Question no – (10)
Solution :
(i) Let, C.P = x
∴ x + x × 8/100 = 168.48
= 100x + 8x/100 = 168.48
= 1084/100 = 16848/100
= x = 16848/100 × 100/108
= x = 156
Therefore, the Cost price will be Rs. 156
(ii) S.P = Rs 1947.80
loss = 10%
Cost Price,
= 1947.8/10 × 100/90
= 19478/9
= 2164.22
Hence, the Cost price will be Rs. 2164.42
(iii) Selling Price = Rs 247.20
Loss = 9%
Now,
C.P = 247.20 × 100/100 – 72
= 24720/10 × 100/28
= 6180/7
= 882.86
Therefore, the cost price will be Rs 882.86
(iv) Selling price = Rs 742.60
Loss = 9%
Now,
C.P = 742.60 × 100/100 – 9
= 7426/10 × 100/9
= 74260/91
= 816.04 Rs.
Thus, the Cost price will be 816.04 Rs.
(v) Selling price = Rs 698.70
Loss = 26 1/2%
Now,
C.P = 698.70 × 100/100 – 37
= 6987/10 × 2 × 100/2530
= 139740/253
= 552.33
Thus, the Cost price will be 753.96 Rs
(vi) Selling price = Rs 475
Loss = 37%
Now,
C.P = 475 × 100/100 – 37
= 475 100/63
= 47500/63
= 753.96
Thus, the Cost price will be 753.96 Rs
Question no – (11)
Solution :
First, Cost Price,
= 300 × 12
= 3600
Profit = 15 %
Now the Selling Price,
= 100 + 15/100 × 3600
= 115 × 36
= 4140
Thus, the selling price of the book will be Rs 4140
Question no – (12)
Solution :
Cost Price,
= 1600 × 3.75/1200
= 500
Selling Price,
= ( 900 × 1/2) + [(1600 – 900) × 2/5)
= 900 × 1/2 + 600 × 2/5
= 450 + 280
= 730
Now the gain Percent (%),
= (730 + 500 / 500 × 100)
= 230/5 %
= 46%
Thus, her gain percent will be 46%
Question no – (13)
Solution :
Loss on 1 dozen,
= 4/100 × 500
= 20 paise
S.P. of 1 dozen orange,
= ( 500 – 20 )
= 480 paise
Selling Price of 1 orange,
= 480/12
= 40 paise
Therefore, the selling price of 1 orange will be 40 paise.
Question no – (14)
Solution :
Let, he must sell x for a rupee
∴ 1/x = 20/5100
= x = 5
∴ He must sell 5 for a rupee.
Question no – (15)
Solution :
First, C.P. of 2 dozen oranges
= 5.50 + 6.50
= 12
Now, S.P. of 2 dozen oranges
= (2 × 7.50)
= 15
Therefore, gain percent(%)
= (3/12 × 100)
= 25%
Question no – (16)
Solution :
Cost Price,
= ( 150 × 10 ) + 100
= 1600
Selling Price,
= 150 × 2 × 1.20
= 2160
Now the gain,
= 2160 – 1600
= 560
Therefore, gain%
= 560/1600 × 100
= 35%
Question no – (17)
Solution :
According to the question,
A fan was bought for = Rs 60
Sold at a loss of = 15%
First Loss,
= 60 × 15/100
= 9
Now, the selling price,
= 60 – 9
= 51
Thus, the selling price of the fan is Rs 51.
Question no – (18)
Solution :
Total Cost price,
= 400 + 40
= 440
Now Profit,
= 400 × 10/100
= 44
∴ Selling Price,
= 440+ 44
= 484
So, the selling price of the radio-set will be Rs. 484
Question no – (19)
Solution :
Total Cost price,
= 2750 + 50
= 2800
= loss 10%
∴ loss,
= 2800 × 10/100
= 280
∴ Selling Price,
= ( 2800 – 280 )
= 2520
∴ Selling price of 1 kg,
= 2520/500
= 5.04 Rs.
Question no – (20)
Solution :
In the question,
A scooter is sold at a loss of 8 1/3%
= 8 1/3%
= 25/3%
∴ Cost Price of the scoter,
= 8250 × 100/100 – 25/3
= 8250 × (100 × 3/275)
= 9000
Thus, the cost price of the scooter will be Rs 9000
Question no – (21)
Solution :
First we find the Cost Price,
= 36000 + 2400
= 38400 Rs
Now, the Selling Price,
= 38400 × (100 – 4/100)
= 384 × 96
= 36864 Rs
Therefore, he sell the house in 36864 Rs
Question no – (22)
Solution :
First, Total C.P,
= ( 3150 × 20 ) + 250
= 63000 + 250
= 63250 Rs.
∴ S.P = ( 3500 × 20 )
= 70000
∴ His total profit,
= ( 70000 – 63250 )
= 6750 Rs.
Question no – (23)
Solution :
According to the question,
Buy 11 stick for 40
Buy 1 stick for 40/11
Sell 10 stick for 44
Sell 1 stick for 44/10
His gain,
= 44/10 – 40/11
= 484 – 400/110
= 84/10
∴ Gain Percent (%),
= ( 84/100 ) / ( 40/11 ) × 100
= (84/110) × (11/40) × 100
= 21%
Thus, his gain percent will be 21%
Question no – (24)
Solution :
First, (4 + 5) = 9 kg costs
= (4 × 20 + 5 × 30)
= 230
1 kg costs
= 230/9
= 25..55
and,
8 kg for (45 × 8)
= 360
= 1 kg for 360/8
= 45
Now, his gain,
= (45 – 25.55)
= 19.45
∴ His gain percent (%)
= 19.45/25..25 × 100
= 38900/511
= 76.12%
Therefore, his gain percent will be 76.12%
Question no – (25)
Solution :
According to the question we know,
She bought bananas at 2 for 1 rupee
She bought bananas at 1 for 1/2 rupee
She bought bananas at 3 for 1 rupee
She bought bananas at 1 for 1/3 rupee
∴ Total coat for 2 bananas,
= 1/3 + 1/2
= 5/6
Now,
Sold 5 bananas for 2 rupees
Sold 1 bananas for 2/5 rupees
∴ Sold 2 bananas for,
= 2 × 2/5
= 4/5 rupee
∴ Her loss,
= 5/6 – 4/5
= 25 – 24 / 30
= 1/30
∴ Her loss percent (%)
= 1 / (3 × 5/6) × 100
= 6 / (30 × 5) × 100
= 4%
Question no – (26)
Solution :
First we find,
C.P = 18 × 25
= 990 Rs
S.P = ( 12 × 65 ) + [ (18 – 12) × 50]
= 780 + (6× 50)
= 780 + 300
= 1080 Rs
∴ His gain,
= 1080 – 990
= 90 Rs
∴ His gain Percent (%)
= 90/990 × 100
= 100/11
= 9 1/11%
Thus, his gain percent will be 9 1/11%
Question no – (27)
Solution :
First, Ramesh S.P,
= 450 × 110/100
= 495 Rs
Now, Amit S.P,
= 495 × 90/100
= 4455/10
= 445.5 Rs
∴ Rahul buy the bicycle 445.5 rupee.
Question no – (28)
Solution :
(a) This statement is True.
(b) This statement is False.
(c) This statement is True.
(d) This statement is True.
(e) This statement is False.
Question no – (29)
Solution :
(i) Profit %
= 150/600 × 100
= 25%
(ii) S.P.
= 370 + 30 + 50
= 450
Profit
= 50/370 ×100
= 500/37
= 12 1/2 %
(iii) C.P.
= 55 + 5
= 60
Loss %
= 10%
Loss = 10/100 × 60
= 6
∴ S.P.
= 60 – 6
= 54
(iv) C.P.
= 3000 + 100
= 3100
Loss
= 160
Loss%
= 160/3100 × 100
= 160/31
= 5 5/31 %
S.P.
= 3100 – 160
= 2940
(v) C.P.
= 640 + 120
= 760
Profit %
= 190*760 × 100
= 25%
S.P.
= 760 + 190
= 950
(vi) C.P.
= 300 + 200
= 500
Profit
= 12%
Profit
= 12/100 × 500
= 60
∴ S.P.
= 500 + 60
= 560
Question no – (30)
Solution :
(i) If the selling price is more than the cost price, then the goods are sold with Profit.
(ii) If the selling price is less then the cost price, than the goods are sold with Loss.
(iii) Loos or gain is calculated on Cost price of the goods.
(iv) SP = CP + Profit (when there is a profit)
(v) SP = CP – Loss (when there is a loss)
(vi) Gain % = x/C.P. × 100 , where x = Gain.
(vii) Loss% = Loss/x × 100, where x = Cost Price
Percentage Profit and Loss Simple Interest Exercise 9.4 Solution
Question no – (1)
Solution :
(i) Principal = Rs 2500 .
Rate = 5%
Time = 1 year
Now, S.I.
= P.R.T /100
= 2500 × 5 × 1 /100
= 125
∴ Amount,
= 2500 + 125
= 2625 Rs
Thus, the simple interest is Rs 125 and amount is Rs 2625
(ii) Principal = Rs 3500
Rate = 6%
Time = 3 year
Now, Simple Interest,
= 3500 × 6 × 3 /100
= 630 Rs
∴ Amount,
= 3500 + 630
= 4130 Rs
Therefore, the Simple Interest is Rs 630 and Amount is Rs 4130
(iii) Principal = Rs 5500,
Rate = 7%,
Time = 2 1/2 year.
Now Simple Interest,
= 5500 × 7 2 1/2 / 100
= 55 × 7 × 5/2
= 1925/2
= 962.50 Rs
∴ Amount,
= 5500 + 962.50
= 6462.50 Rs
Hence, the Simple Interest is Rs 962.50 and Amount is Rs 6462.50
(iv) Principal = Rs 3785,
Rate = 12%
Time = 3 1/2
Now Simple Interest,
= 3785 × 12 × 3 1/2 /100
= (3785 × 12 × 7) / (100 × 2)
= 158670/10
= 1589.70 Rs
∴ Amount,
= (3785 + 1589.70)
= 5374.70 Rs
Thus, Simple Interest is Rs 1589.70 and Amount is Rs 5374.70.
(v) Principal = Rs 4500,
Rate = 6%
Time = 9 months.
First, 9 month
= 9/12 years
= 3/4 years
Now Simple Interest,
= (4500 × 6 × 3/49) × 100
= 405/2
= 202.50 Rs
∴ Amount,
= 4500 + 202.50
= 4702.50 Rs
Hence, the Simple Interest is Rs 202.50 and Amount is Rs 4702.50
(vi) Principal = Rs 2550
Rate = 7%
Time = 156 days = 156/365
Now Simple Interest,
= (2500 × 7 × 156) / 5100 × 365
= 27846/365
= 76.29 Rs
∴ Amount,
= 2500 + 76.29
= 2626.29 Rs
Therefore, the Simple Interest is Rs 76.29 and Amount is Rs 2626.29
(vii) Principal = Rs 730
Rate = 4 /12% = 9/2%
Time = 62 days = 62/365
∴ Simple Interest,
= (730 × 9 × 62) × (100 × 2 × 365)
= 279/50
= 5.58 Rs
∴ Amount,
= 730 + 5.58
= 735.58 Rs
Hence, the Simple Interest is Rs 5.58 and Amount is Rs 735.58
(viii) Principal = Rs 3500
Rate = 6%
Time = 240 days = 240/365 = 48/73
Now Simple Interest,
= (3500 × 6 × 48) × (100 × 73)
= 10080/73
= 138.08 Rs
∴ Amount,
= 3500 + 38.08
= 3638.08 Rs
Therefore, the Simple Interest is Rs 138.08 and Amount is Rs 3638.08
Question no – (2)
Solution :
First Simple Interest,
= 5000 × 8 × 1 / 100
= 400 Rs
Now Amount,
= 5000 + 400
= 5400 Rs
Therefore, Anu get after one year 5400 Rs.
Question no – (3)
Solution :
In the question,
Principal = 500 Rs
Time = 3 years
Rate = 7% per annum
Now Simple Interest,
= 500 × 3 × 7 / 100
=105 Rs
∴ Amount,
= 500 + 105
= 605 Rs
Thus, the amount to be paid at the end of the period is 605 Rs
Question no – (4)
Solution :
In the given question,
Principal = 1000 Rs
Time = 3
Rate = 12%
Now Simple Interest,
= 1000 × 12 × 3 / 100
= 360 Rs
∴ Amount,
= 1000 + 360
= 1360 Rs
Hence, the Interest is Rs 360 and the amount is Rs 1360
Question no – (5)
Solution :
1st January to 15 march
=31 + 28 + 15
= 74 days
= 74/365 days
Now Simple Interest,
= (57.5 × 6 × 74) /(1000 × 365)
= 51060/1000 × 73
= 0.69 paise
∴ Amount,
= (57.50 + 0.69)
= 58.19 Rs
Therefore, simple interest is Rs 0.69 paise and amount is Rs 58.19
Question no – (6)
Solution :
According to the question,
Principal = 8000 Rs
Rate = 12 1/2%
Time = 2 year 3 month
= 2 year . (3/12y) ye
= (2+1/4)
= 9/4 year
12 1/2%
= 25/2%
Simple Interest,
= 8000 × 25 × 9 × 1000 × 2 × 4
= 2250 Rs
∴ Amount,
= 8000 + 2250
= 10250 Rs
Therefore, he will receive Rs 10250
Question no – (7)
Solution :
Anil’s Interest,
= 800 × 6 × 3 / × 100
= 144 Rs
Rohit’s interest,
= 900 × 5 × 3 / × 100
= 135 Rs
Anil will get more interest by,
= (144 – 135)
= 9 Rs
Hence, Anil will get more interest by 9 Rs.
Question no – (8)
Solution :
According to the question,
Principal = 365
Time = 300 days
Rate = 8%
Now Simple Interest,
= 365 × 8 × 300/100 × 365
= 24 Rs.
Thus, the simple interest on Rs 365 will be Rs 24
Question no – (9)
Solution :
From the question we get,
Principal = 300 Rs
Rate = 4%
Time = 2 1/2 years
Simple Interest,
= 300 × 4 × 5 / 100
= 30 Rs.
∴ Amount,
= (300 + 30)
= 330 Rs
Therefore, the amount paid by him to the post office is 330 Rs
Question no – (10)
Solution :
1st Feb. 1995 to 24th Sep. 1997
= 28 + 31 + 30 + 31 + 30 + 2 year + 31 + 30 + 24
= 2 year 235 days
= 2 year 345/365
= (2 + 47/73)
= 193/73 year
Now Simple Interest,
= 2300 × 21/2 × 193/73 × 100
= 93219/146
= 638.48 Rs
∴ Amount,
= 2300 + 638.48
= 2938.48 Rs
Therefore, the amount he returned to Punnet is Rs 2938.48
Question no – (11)
Solution :
In the question,
Principal = 2500 Rs
Time = 6
Rate = 9%
Now Simple Interest,
= 2500 × 9 × 6 / 100
= 1350 Rs
∴ Amount,
= 2500 + 1350
= 3850 Rs
Question no – (12)
Solution :
In the given question,
Principal = 3000
Time = 3 years
Rate = 6%
Now Simple Interest,
= 3000 × 3 × 6 / 100
= 540 Rs
∴ Amount,
= 3000 + 540
= 3540 Rs
Therefore, she will get back Rs 3540
Question no – (13)
Solution :
5th July to 16th Sep ……(according to the question)
= 26 + 31 + 16
= 73 days
∴ Simple Interest,
= 625 × 10 × 73 / 100 × 365
= 12.5 Rs
∴ Amount
= (625 + 12.5)
= 637.50 Rs
Hence, the amount Neelu will pay to Kunal is 637.50 Rs
Question no – (14)
Solution :
After 1 year S.I,
= 5000 × 6 × 1 / 100
= 300
∴ Amount,
= 5000 + 300
= 5300 Rs
Withdrew 1500 left,
= 5300 – 1500
= 3800 Rs
After 3 year S.I,
= 3800 × 6 × 2/100
= 456 Rs
∴ Amount,
= 3800 + 456
= 4256 Rs
Thus, his balance after 3 years will be Rs 4256
Question no – (15)
Solution :
From the given question we get,
Principal = 2500 Rs
Time = 4%
Rate = 3 years
Now Simple Interest,
= 2500 × 4 × 3/100 + 500 × 6 × 3/100
= 300 + 90
= 390 Rs
Hence, Interest will he pay after 3 years is Rs 390
Question no – (16)
Solution :
Total interest,
= 10000 × 9 × 1 /100 + 2500 × 9 × 2/100
= 900 + 1350
= 2250 Rs
∴ He will get after
= 10000 + 2250
= 12250 Rs
Question no – (17)
Solution :
In the given question we get,
Principal = 25000 Rs
Time = 1 1/2 years
Rate = 11%
Simple Interest,
= 2500 × 11 × 3 /100 × 2
= 4125
∴ Amount,
= 29125
∴ Cost of T.V.
= (291525 – 26500)
= 2625 Rs.
Therefore, the cost of the TV will be Rs 2625.
Question no – (18)
Solution :
From the question we know,
Principal = 65000 Rs
Time = 12%
Rate = 1 years (every year)
Now Simple Interest,
= 6500 × 12 × 1/100
= 7800 Rs
∴ Value of each scholarship
= 7800/15
= 520 Rs
Hence, the value of each scholarship will be Rs 520
Next Chapter Solution :
👉 Chapter 10 👈
