# Brilliant’s Composite Mathematics Class 6 Solutions Chapter 9

## 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,

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 :

Updated: June 12, 2023 — 5:18 am