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**Maths Wiz Class 8 Solutions Chapter 8 Percentage and its Applications**

Welcome to NCTB Solutions. Here with this post we are going to help 8th class students for the Solutions of Maths Wiz Class 8 Math Book, Chapter 8, Percentage and its Applications. Here students can easily find step by step solutions of all the problems for Percentage and its Applications, Exercise 8A, 8B, 8C, 8D and 8E 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. Here in this post students will get chapter 8 solutions. Here in this post all the solutions are based on ICSE latest Syllabus.

**Percentage and its Applications Exercise 8A Solution :**

**Question no – (1) **

**Solution : **

**(a) 12% of 75**

= 12/100 × 75

= 9

∴ 12% of 75 is 9

**(b) 120% of ₹ 30**

= 120/100 × 30

= 36

**∴** 120% of Rs 30 is Rs 36

**(c) 75% of 8 m**

= 75/100 × 8

= 6

**∴ **75% of 8 m is 6 m

**Question no – (2) **

**Solution : **

**(a) 8 of 32**

= (8/32 × 100) %

= 25%

**(b) 63 of 105**

= 63/105 × 100

= 60%

**(c) -8 of -64**

= (-8/-64 × 100)%

= 25/2%

= 12.5%

**(d) 52 of 4**

= (52/4 × 100)%

= 1300%

**Question no – (3) **

**Solution : **

**(a) 4% is 1.8**

Let, x × 4/100 = 1.8/10

= x = 18 × 5/2

= x = 45

**(b) 90% is 279**

= x × 90/100 = 279

= x = 279 × 10/9

= x = 310

**(c) 120% is 90**

= 120/100 × x = 90

= x = 90 × 10/12

= x = 75

**(d) 15% is 48**

= 15/100 × 48 = 36/5

= 7.2

**Question no – (4)**

**Solution : **

**(a) 0.7**

= (0.7/10 × 100)%

= 70%

**(b) 0.09**

= (0.09/100 × 100)%

= 9%

**(c) 3/4**

= 3/4 × 100)%

= 75%

**(d) 11/25**

= (11/25 × 100)%

= 44%

**(e) 8/8**

= (8/8 × 100)%

= 100%

**(f) 35/100**

= (35/100 × 100)%

= 35%

**(g) 0.94**

= (0.94/100 × 100)

= 94%

**(h) 19/20**

= (19/20 × 100)

= 95%

**(i) 0.002**

= (0.002/1000 × 100)

= 1/5%

**(j) 198/1000**

= (198/1000 × 100)

= 99/5

= 19 4/5%

**Question no – (5) **

**Solution : **

**(a) 27%**

= 247/100

= 0.27

**Note : **

To convert percent to decimal we have to take up the following point

Number 1, for the reason of percent the denominator is 100 is placed – 27/100

To make it decimal first, right 27 and count number of zero after one in denominator.

Here, is 2 zero.

So, the answer is 0.27.

**(b) 44%**

= 44% = 44/100

= 0.44

**(c) 80%**

= 80% = 80/100

= 0.8

**(d) 112%**

= 112% = 112/100

= 1.12

**Question no – (6) **

**Solution : **

1/2% = 1/200

= 0.005

= 0.5 is greater than 0.005

**Question no – (7) **

**Solution : **

**(a) 50 to 60**

**∴** 50 to 60 = (60 – 50/50 × 100)%

= 10 × 2%

= 20%

**(b) 9 to 45**

**∴** 9 to 45 = (45 – 9/9 × 100)%

= 36/9 × 100

= 400%

**(c) 400 to 300**

**∴** 400 to 300 = (400 – 300/400 × 100)%

= 100/4%

= 25%

**(d) 300 to 275**

**∴** 300 to 275

= (300 – 275/300 × 100)%

= 25/3

= 8 1/3%

**Question no – (8) **

**Solution : **

As per the question,

The cost of a book was = ₹ 350

The bookseller gave me = 20% discount

**∴** 350 × 80/100

= 280 Rs

Therefore, I paid Rs. 280 for the book.

**Question no – (9) **

**Solution :**

Let the original price = x

**∴** x × 70/100 = 2100

= x = 2100 × 10/7

= 3000

Therefore, the sweater original price was Rs. 3000

**Question no – (10) **

**Solution : **

According to the question,

= (480 – 360/480 × 100)%

= (120/480 × 100)%

= 25%

Therefore, the percent change in sodium content will be 25%

**Question no – (11) **

**Solution : **

As per the given question,

A person insures goods in his house valued at ₹ 5 lakh

**The rate of 5 percent, **

**∴** (500000 × 5/100)

= 25,000

Hence, He paid 25,000 rupees annual premium.

**Question no – (12) **

**Solution :**

According to the question,

The customs duty on an item is 33 1/3% of its value

**∴** 5100 × 100/3 × 1/100

= 1700 Rs

Therefore, the custom duty will be 1700 rupees.

**Question no – (13) **

**Solution :**

As per the question,

Candidates appeared for an examination = 3000

Passed = 92%

**∴** 3000 × 92/100

= 1860

Therefore, 1860 candidates are passed.

**Question no – (14) **

**Solution : **

Let, the marked price is x

= x × 95/100 = 7600

= x = 7600 × 100/95

= 8000 Rs

Hence, the marked price will be Rs 8000

**Question no – (15) **

**Solution : **

= (8/32 × 100)

= 25 Rs

Hence, 25 matches did they play in all.

**Question no – (16) **

**Solution : **

**(a)** A shirt marked at Rs 960

= 960 × 70/100

= 672 Rs

**(b)** A pair of shoes marked at Rs 870

= 870 × 70/100

= 609 Rs

**(c)** A jacket marked at Rs 4500

= 4500 × 70/100

= 3150 Rs.

**Percentage and its Applications Exercise 8B Solution :**

**Question no – (1) **

**Solution : **

Percent of the people like other games,

= (100 – 45 – 40)%

= 15%

**∴**** Like football,**

= 4,00,000 × 45/100

= 180000

**Like cricket,**

= 400000 × 40/100

= 160000

**Like other games,**

= 400000 × 15/100

= 60000

**Question no – (2) **

**Solution : **

96% students passed

**∴** 4% students failed = 500 students

**∴** 1% student = 500/4 = 125 students

**∴** 100% students = 12500 students appeared at the exam.

**Question no – (3) **

**Solution : **

**Let,** the third number be 100

Then 1st number = 112 1/2 = 225/2

2nd number = 125

**Require (%)** = (1st number/2nd number × 100)%

= (225/2 × 1/125 × 100)

= 90%

Therefore, the first number is __90%__ of the second number.

**Question no – (4) **

**Solution : **

Let his monthly income = x

**∴** his annual income = 12x

**∴** Given 26/100 × 12x = 89856

= x = 89856 × 100/26 × 12

= 28800 Rs

Therefore, his monthly income will be Rs 28800.

**Question no – (5) **

**Solution : **

Let the number be = x

**∴** Given, x × 54/100 – x × 26/100 = 22526

= x/100 {54 – 26} = 22526

= x × 28 = 22526 × 100

= x = 22526/28 × 100

= 804500

Therefore, 66% of that number will be __804500__

**Question no – (6) **

**Solution : **

Let the number be x

**∴** Given, x – 125 = x × 37.5%

= x – 125 = x × 375/1000

= x – 375x/1000 = 125

= 1000x – 375x/1000 = 125

= 625x = 125000

= x = 125000/625

**∴**** 25% of 200**

= 200 × 25/100

= 50

Thus, 25 percent of this number will be __50__

**Question no – (8) **

**Solution :**

Let the price of article is 100 rupees

**∴**** 25% of 100**

= 125/100 × 100

= 125

**∴**** 20% of 125**

= 120/100 × 125

= 150

**Price increase, **

= (150 – 100)

= 50 rupees

**∴**** Total percent increase, **

= (150 – 125/50 × 100)%

= (25/50 × 100)%

= 50%

Therefore, the total percent increase is __50%__

**Question no – (9) **

**Solution : **

Let B’s amount = x

C receives 25% less than B

= x × 75/100

**A receives 25% more than**

= x × 75/100 × 125/100

**Given,** x × 75/100 × 125/100 + x × 75/100 + x = 2236

= 15x/16 + 3x/4 + x = 2236

= 15x + 12x + 16x/16 = 2236

= 43x = 2236 × 16

= x = 2236 × 16/43

= 332

**∴**** A’s share in the amount,**

= 332 × 3/4 × 5/4

= Rs 780

Therefore, A’s share in the amount will be __Rs 780__

**Question no – (10) **

**Solution : **

Let the number of workers =100

75% skilled workers = 100 × 75/100 = 75

**∴**** 80% of skilled workers are permanent, **

= 75 × 80/100

= 60

**25% unskilled workers**

= 100 × 25/100

= 60

**20% of unskilled workers are permanent**

= 25 × 20/100

= 5

**∴** 65 are permanent

**∴** 35 are temporary

Let the total number of workers is x

**∴**** x × 35/100 = 126**

= x = 126 × 100/35

= 360

Therefore, Total number of workers are 360

**Question no – (11) **

**Solution : **

Let the total number of exam = x

Given, (30x/100 + 15) = (40x/100 – 35)

= 3x/10 + 15 = 4x/10 – 35

= 4x/10 – 3x/10 = 35 – 15

= x/10 = 50

= x = 500

**∴**** Minimum per cent pass marks, **

= (30 × 500/100 + 15)%

= (150 + 15)%

= 165%

Therefore, the minimum percent pass marks is 165%

**Question no – (12) **

**Solution : **

Let the total number of votes polled is x

**∴** x = 432 × 100/62

62% of total votes for win

**∴** Another candidate get 38% of total vote

**∴** x × 38/100 + 432 = x × 62/100

= 62x/100 – 38x/100 = 432

= 24x/100 = 432

= x = 432 × 100/24

= 1800

Therefore, the total number of votes polled is __1800__

**Question no – (13) **

**Solution : **

Let the total number of votes = x

one person get 52% and won

**∴** another person get 48% and loss

**∴** x × 48/100 + 98 = x × 52/100

= 52x/100 – 48x/100 = 98

= 4x/100 = 98

= x = 98 × 100/4

= 2450

**∴** 68 votes were declared invalid

**∴** (2450 + 68) = 2518 are total number of vote polled.

Therefore, the total number of votes are __2518__

**Percentage and its Applications Exercise 8C Solution :**

**Question no – (1) **

**Solution : **

According to the question,

Article cost price = ₹ 225

overhead expenses = ₹ 15 is

Selling Price = ₹ 300.

**∴**** Profit percent, **

= (300 – 225/300 × 100)

= 75/300 × 100

= 25%

Hence, the the profit percent will be 25%

**Question no – (2) **

**Solution : **

As per the question,

Selling price article for = ₹ 960

Incurs a loss of = 4%.

**∴ Cost Price of the article, **

= (100/100 + Gain%) × S.P

= (100/100 – 4) × 960

= 100/96 × 960

= 1000 Rs

Therefore, the cost price of the article will be 1000 Rs.

**Question no – (3) **

**Solution : **

Let selling price = 100 Rs

**∴ **C.P = 80/100 × 100

= 80 Rs

**∴ Profit %**

= (100 – 80/80 × 100)%

= (20/80 × 100)%

= 25%

Therefore, the profit percent will be 25%

**Question no – (4) **

**Solution : **

As per the question,

100 orange bought for = 350

1 orange bought for

= 350/100

= 35/10

**∴** 12 orange bought for

= 35/10 × 12

= 42

But He selling 48 rupees per dozen

**∴** **Profit,**

= (48 – 42)

= 6

**∴**** Profit (%),**

= (6/42 × 100)%

= 100/7

= 14 2/7 % profit

Therefore, the percentage of profit will be 14 2/7 %

**Question no – (5) **

**Solution : **

Let the price of one article is x

**∴**** Profit,**

= (25x – 20x)

= 5x

**∴**** Profit (%)**

= (5x/20x × 100)%

= 25%

**Question no – (6) **

**Solution : **

As per the given question,

11 book purchased for = Rs 1000

1 book purchased for 1000/11

10 book purchased for 1000 × 10/11

and 10 books sell for 1100

**∴**** Profit, **

= 1100 – 10000/11

= 12100 – 10000/11

= 2100/11

**∴**** Profit (%),**

= (2100/11 × 11/1000 × 10 × 100)%

= 21%

**Question no – (7) **

**Solution : **

Let the cost price of the article = x

∴ Given that,

x × 80/100 + 650 = x × 120/100

= 8x/10 + 60 = 12x/10

= 12x/10 – 8x/10 = 60

= 4x/10 = 60

= x = 60 × 10/4

= 150 Rs

Therefore, the cost price of the article will be 150 Rs.

**Question no – (8) **

**Solution : **

Let the cost price of the table = x

10% profit = x × 110/100 = 11x/10

5% of less cost = x × 95/100 = 95x/100

**∴** 20% profit = 95x/100 × 120/100 = 114x/100

**Given, **11x/10 + 80 = 114x/100

= – 11x/10 + 114x/100 = 80

= – 110x + 114x/100 = 80

= 4x = 80 × 100

= x = 80 × 100/4

= 2000 Rs

Therefore, the cost price of the table will be Rs 2000.

**Question no – (9) **

**Solution : **

C.P of car sold 20% loss

= 100/80 × 120000

= 150000

C.P of jeep sold 20% gain

= 100/120 × 120000

= 100000

**∴**** Total Cost Price, **

= (150000 + 100000)

= 250000

**Total Selling Price, **

= (120000 + 120000)

= 240000

**∴** Since C.P > S.P there is a loss

**∴** Loss = 25000 – 240000

= 10,000 Rs.

Hence, the overall loss will be 10,000 Rs.

**Question no – (10) **

**Solution : **

Let the C.P and S.P are 20x and 21x

**∴**** Profit**

= (21x – 20x)

= x

**∴**** Profit (%)**

= (x/20x × 100)%

= 5%

Therefore, the gain percent will be 5%.

**Question no – (12) **

**Solution : **

Let the C.P = x

**∴**** Given,**

x × 91/100 = 105

x = 105 × 100/91

= 1500/13

**∴**** For 30% gain**

= (1500/13 × 130/100)

= 150 rupees

Therefore, the article must be sold at **150** rupees

**Question no – (13) **

**Solution : **

Profit = selling price of 15 articles

**∴**** C.P = selling price of,**

= (60 – 15)

= 45 articles

**∴**** Gain percentage,**

= (15/45 × 100) %

= 100/3

= 33 1/3%

Therefore, his gain percentage will be 33 1/3%

**Question no – (14) **

**Solution : **

Let the cost price of gain watch = x

**∴** The cost price of loss watch = (850 – x)

**∴** 16% gain = 116/100 × x = 116x/100

12% loss = 88/100 (840 – x)

= 88 × 840/100 – 88x/100

**Given there is no profit or no gain**

**∴** 116x/100 + 88 × 840/100 – 88x/100 = 840

= 28x/100 + 88 × 840/100 = 840

= 28x + 88 × 840 = 84000

= 28x = 84000 – 88 × 840

= x = 84000/28 – 88 × 840/28

= 3000 – 2640

= 360

Therefore, the cost price of the watch will be Rs 360.

**Question no – (15) **

**Solution : **

Let the goods C.P = 100

20% gain he buying the good

= 100 × 80/100

= 80 Rs

**And gain 30% while selling, **

= (80 × (100 – 30)/100)

= 80 × 70/100

= 56%

Therefore, his total gain percent will be 56%

**Question no – (17) **

**Solution : **

Profit of 10%

= 10000 × 110/100

= 11000 Rs

Loss of 10%

= 10000 × 90/100

= 9000 Rs

**∴**** Total selling Price, **

= (11000 + 9000)

= 20000 Rs

**∴**** Total cost Price, **

= (10000 + 10000)

= 20000 Rs

**∴** There is neither profit nor loss.

**Question no – (18) **

**Solution : **

1^{st} discount 25% and 2^{nd} discount of 30% over an above the existing discount.

**∴** She pay for it = 1200 × 75/100 × 70/100

= 30 × 3 × 7

= 630

Therefore, she will pay Rs 630 for it.

**Percentage and its Applications Exercise 8D Solution :**

**Question no (1) **

**Solution : **

**(a)** I = P.R.T/100

= 340 × 3 × 6/100

= 63

**∴**** Simple Interest (S.I)** = Rs 63,

**∴**** Amount** = (350 + 63) = Rs 413

**(b)** I = 765 × 16/3 × 5/2/100

= 765 × 16 × 5/ 3 × 2 × 100

= 102

**∴** Simple Interest (S.I) = Rs 102

**∴** Amount,

= (765 + 102)

= Rs 867

**(c)** 4 months = 4/12 = 1/3 year

**∴** 2 year 4 months,

= (2 + 1/3) year

= 7/3

**∴** I = 475 × 7/3 × 9/2/100

= 475 × 7 × 9/26 × 100

= 399/8

= 49.875

**∴**** Simple Interest (S.I)** = Rs 49.875

**∴**** Amount **= (475 + 49.875)

= Rs 524.875

**(d)** 20 months = 20/12 year = 5/3

**∴** I = 1900 × 5/3 × 6/100

= 190

**∴**** Simple Interest (S.I)** = Rs 190

**∴**** Amount **= (1900 + 190)

= Rs 2090

**(e)** April = 25, may – 31, Jun – 24

**∴** time = 25 + 31 + 24/365 year

= 80/365 year

I = 7300 × 80/365 × 5/100

= 80

**∴**** Simple Interest (S.I) **= Rs 80

**∴**** Amount **= (7300 + 80)

= Rs 7380

**Question no – (2) **

**Solution : **

Given, P = 800,

I = 80,

t = 2 years

r = ?

We know, I = PRT/100

= r = 100 × I/Pt

= 100 × 80/800 × 2

= 5%

Hence, the rate percent will be 5%

**Question no – (3) **

**Solution : **

As per the given question,

P = 600,

I = 48,

r = 4%,

T = ?

**∴**** We know that, **I = p r t/100

= t = 100 × I/pr

= 100 × 48/600 × 4

= 2 years

Therefore, the required time will be 2 years.

**Question no – (4) **

**Solution : **

According to the question,

I = 231,

t = 3,

r = 7%

P = ?,

As we know, I = p r t/100

= P = 100 × I/RT

= 100 × 231/3 × 7

= 100

Therefore, the required sum of money will be Rs __100__

**Percentage and its Applications Exercise 8E Solution :**

**Question no – (1)**

**Solution : **

According to the given question,

P = 6000 Rs

t = 2,

r = 10%

**For the first year,**

P = 6000, t = 1, r = 10%

I = 6000 × 1 × 10/100 = 600

**∴** amount = 6600 Rs

**For the 2nd year,**

P = 6600, t = 1, r = 10%

I = 6600 × 1 × 10/100 = 660

**∴**** Amount,**

= (6600 + 660)

= 7260 Rs

**∴**** C.I**

= (7260 – 6000)

= 1260 Rs

Hence, the compound interest will be 1260 Rs

**Question no – (2) **

**Solution : **

**For the 1st year,**

P = 15000, t = 1, r = 8%

I = 15000 × 1 × 8/100 = 1200

**∴** amount = (15000 + 1200) = 16200

**For the 2nd year,**

P = 16200, t = 1, r = 8%

I = 16200 × 1× 8/100 = 1296

**∴ Amount,**

= (16200 + 1296)

= 17496 Rs

**∴ C.I.**

= (17496 – 15000)

= 2496 Rs

Thus, the compound interest will be 2496 Rs

**Question no – (3) **

**Solution : **

**For the 1st year**

P = 50,000, t = 1, r = 10

I = 50000 × 1 × 10/100 = 5000

∴ Amount,

= (50000 + 5000)

= 55000 Rs

**For the 2nd year**

P = 55000, t = 1, r = 10

I = 55000 × 1 × 10/100 = 5500

∴ Amount,

= (55000 + 5500)

= 60500 Rs

**For the 1/2 year**

P = 60500, t = 1/2, r = 10

I = 60500 × 1/2 × 10/100 = 3025

**∴** Amount

= (60500 + 3025)

= 63525 Rs

**∴**** Compound Interest, **

= (63525 – 50000)

= 13,525 Rs

Therefore, the compound interest will be 13,525 Rs]

**Question no – (4) **

**Solution : **

**First 1/2 year**

P = 16000, r = 10, t = 1/2

I = 16000 × 10 × 1/2/100 = 800

∴ Amount,

= (16000 + 800)

= 16800 Rs

**For the 2nd 1/2 year**

P = 16800, r = 10, t = 1/2

I = 16800 × 10 × 1/2/100 = 840

**∴** Amount,

= (16800 + 840)

= 17640 Rs

**For the 3rd 1/2 tear**

P = 17640, r = 10, t = 1/2

I = 17640 × 10 × 1/2/100 = 882

∴ Amount,

= (17640 + 882)

= 18522 Rs

**∴**** C.I,**

= (18522 – 16000)

= 2522 Rs

Hence, the compound interest will be 2522 Rs.

**Question no – (5) **

**Solution : **

**For the 1st year,**

P = 15000,

t = 1,

r = 8%

I = 15000 × 1 × 8/100 = 1200

**∴** Amount,

= (15000 + 1200)

= 16200 Rs

**For the 2st year,**

P = 16200,

t = 1,

r = 9

I = 16200 × 1 × 9/100 = 1458

**∴** Amount,

= (16200 + 1458)

= 17658 Rs

**∴**** C.I,**

= (17658 – 16200)

= 1,458 Rs

Thus, the compound interest will be 1,458 Rs

**Question no – (6) **

**Solution : **

**(a)** As per the given question,

P = 40,000 Rs

t = 2,

r = 9

= 40,000(1 + 9/100)^{2}

= 40,000 109 × 109/100 × 100

= 47524 Rs

**∴**** C.I.**

= (47524 – 40,000)

= 7524 Rs

Therefore, the compound interest will be 7524 Rs.

**(b) **According to the question,

P = 5000 Rs

t = 2 year,

r = 10

**Amount** = 5000 (1 + 10/100)^{2}

= 5000 × 11 × 11/10 × 10

= 6050 Rs

**∴** C.I = (6050 – 5000)

= 1050 Rs

Thus, the compound interest will be 1050 Rs.

**(c)** Given in the question,

P = 10,752 Rs

t = 3,

r = 12 1/2% = 25/2

**∴ Amount** = 10752 (1 + 25/2/100)^3

= 10752 (1 + 1/8)^3

= 10752 9×9×9/8×8×8

= 15309 Rs

**∴ C.I.** = (15309 – 10752)

= 4557 Rs.

Therefore, the compound interest will be 4557 Rs.

**Question no – (7) **

**Solution : **

**For 1st, 1/2 year,**

P = 256,

r = 25/2% ,

t = 1/2

**∴** I = 256 × 25/2 × 1/2/100

= 16 Rs

**∴** Amount = (256 + 16)

= 272 Rs

**For 2nd, 1/2 year,**

P = 272,

r = 25/2,

t = 1/2

I = 272 × 25/2 × 1/2/100

= 17 Rs

**∴** Amount = (272 + 17)

= 289 Rs

**∴**** C.I.** = (289 – 256)

= 33 Rs

Hence, the compound interest will be 33 Rs.

**Question no – (8) **

**Solution : **

Compound interest half-yearly

R = 10/2 % = 5%,

T = 1 1/2 year = 3 half years

**∴** Amount = 24000 × (1 + 5/100)3

= 24000 × 21 × 21 × 21/20 × 20 × 20

= 27783 Rs

**∴**** C.I.** = (27783 – 24000)

= 3783 Rs

Therefore, the amount will be Rs 27783 and the compound interest will be Rs 3783

**Question no – (9) **

**Solution : **

Compounded half-yearly

r = 12.5/20 1 1/2 year = 3 year halfly

**∴**** Amount, **

= 8192 (1 + 125/20 × 100)3

= 8192 (1 + 1/16)3

= 8192 × 17/16 × 17/16 × 17/16

= 9826 Rs

Therefore, the amount that Anirudh had to pay will be Rs. 9826

**Question no – (10) **

**Solution : **

P = 80,000, t = 3, R_{1} = 4%, R_{2} = 5%, R_{3} = 10%

A = P(1 + R_{1}/100) (1 + R_{2}/100) (1 + R_{3}/100)

= 80,000 (1 + 4/100) (1 + 5/100) (1 + 10/100)

= 80,000 × 104/100 × 105/100 × 110/100

= 96,096 Rs

**∴ C.I.** = (96096 – 80,000)

= 16096 Rs

Therefore, the compound interest will be 16096 Rs.

**Next Chapter Solution : **

👉 Chapter 9 👈