Chapter : 8Chapter : 8Comparing quantitiesComparing quantities

Exercise : 8.1 q.1: Find ratio of the following : (a): Speed of a cycle 15 km per hour

to the speed of scooter 30 km per hour .Sol : Ratio = 15 km : 30 km = 15 : 30 = 15/30 = 1/2 = 1 : 2

(b) : 5 m to 10 km . Sol : Ratio = 5 m : 10 km = 5 m : 10000 m = 5 : 10000 = 5/10000 = 1/2000 = 1 : 2000

(c) : 50 paise to Rs 5 .Sol : Ratio = 50 paise : Rs 5 = 50 paise : 500 paise = 50 : 500 = 50/500 = 1/10 = 1: 10

Q.2 : Convert the following ratio to % :

(a) : 3 : 4 Sol : 3 : 4 % = 3/4 = 3/4 x 100 = 75 % 2 : 3 Sol : 2 : 3 % = 2/3 = 2/3 x 100 = 66 2/3 %

(b) :

Q.3 : 72 % of 25 students are good in Mathematics . How many are not good in Mathematics ?

Sol : No. of st. good in maths = 75 % No. of st. not good in maths = (100

– 72) = 28 %

of 25 =

28/100 x 25 = 7 st.

Q.4 : A football team won 10 matches out of the total no. of matches they played . If their win % was 40 , then how many matches did they play in all ?

Sol : Let they played games in all be x . The no. of games won by f.b. t.= 40% of x = 40/100 x (x) = 2x According to the Q. : 2x/5 = 10 x = 10 x 5/2 = 25 Therefore, 7 st. are not good in Mathematics.

Q.5 : If Chameli had Rs 600 left after spending 75% of her money, how much did she have in the beginning ?

Sol : let the t.money she had in the beginning was Rs x.

The money she had spent = 75% of Rs x

= 75/100 x (x)

= Rs 3x/4 Money she had left = Rs x – Rs 3x/4 = Rs {x – 3x/4} = Rs

x/4

According to the question ; x / 4 = 600 x = 600 x 4 = Rs 2400 Therefore , the money she had in

the beginning was Rs 2400 .

q.6 : If 60% people in a city like cricket, 30% like football and the remainig like other games then what % of the people like other games ? If the total no. of people are 50 lakh, find the exact no. who like each type of game ?

Sol :% of p. like o.game = [100 – (60+ 30)%

= (100 – 90) % = 10 %

Total no. of people = 50 lakh = 50,00,000 No. of people like cricket = 60 % of 50,00,000 = 60/100 x 50,00,000 = 3,00,000= 3 lakh No. of people like football = 30% of 50,00,000 = 30/100 x 50,00,000 = 15,00,000 = 15 lakh

No. of like people o. games = 10% of

5000000 = 10/100 x

5000000 = 5,00,000 =

5 lakh Therefore, 3 lakh people like cricket,

15 lakh people like football & 5 lakh people like other games .

Exercise : 8.2Q.1 : A man got a 10% increase in his

salary . If tis new salary is Rs 1,54,000, find his original salary ?

Sol : Let his original salary be Rs (x) . Increase in his salary = 10% of Rs

(x) =10/100 x (x) = Rs x/10

New salary = o. salary + i. salary = Rs x + Rs x/10 = Rs 11x/10 According to the question ; 11x/10 = 154000 (x) = 154000 x 10/11 (x) = 1,40,000 Therefore, his original salary is Rs

1,40,000.

Q.2 : On Suday 845 people went to the Zoo. On Monday 169 people went . What is the % decrease in the visiting the Zoo on Monday?

Sol : No. of people went to Zoo on Sunday

= 845 people No. of people went to Zoo on

Monday = 169 people

Decrease in no. of people visiting the Zoo

= 845 – 169 ( people )

= 676 people % decrease in the no. of people visiting

the Zoo = 676/845 x 100% = 80% Therefore, the % decrea % .se in the

people visiting the Zoo on Monday is

Q.3 : A shopkeeper buys 80 articles for Rs 2,400 and sells them for a profit of 16 %. Find the selling price of one article ?

Sol : C.P. of 80 articles = Rs 2,400 Profit = 16 % of Rs

2,400 = 16/100 x 2,400 = Rs 384

S.P. of 80 articles = C.P. + Profit = Rs 2,400 + Rs

384 = Rs 2,784 S.P. of 1 article = Rs 2,784/80 = Rs 34.80 Therefore, the selling price of one

article is Rs 34.80

q.4 : The cost of an article was Rs 15,500, Rs 450 were spent on its repairs . If it is sold for a profit of 15%, find the selling price of the article ?

Sol : C.P. of an article = Rs 15,500 + Rs 450

= Rs 15,950 Profit = 15% of Rs 15,950 = 15/100 x 15,950 =Rs 2,392.50

S.P. of an article = C.P. + Profit = Rs 15,950 +

Rs2,392.50 = Rs 18,342.50 Therefore, the selling price of

the article is Rs 18,342.50

q.5 : A VCR and TV were bought for Rs 8,000 each. The shopkeeper made a loss of 4% on the VCR and a 8% on the TV. Find thegain or loss % on the whole transaction ?

Sol : Combined C.P. of the both VCR and

TV = Rs 8,000 + Rs 8,000 = Rs 16,000 Loss of 4% on the VCR = 4/100 x

8,000 = Rs 320

S.P. of the VCR = C.P. – Profit = 8,000 – 320 = Rs 7,680 Profit of 8% on the TV = 8/100 x

8,000 = Rs 640 S.P. of the TV = C.P. + Profit = 8,000 + 640 = Rs 8,640

Combined S.P. = Rs 7,680 + Rs 640 = Rs 16,320 Gain of the whole transaction = S.P. – C.P. = Rs 16,320 – Rs

16,000 = Rs 320 Gain % = 320/16,000 x100 = 2% Therefore, the gain % on the whole

transaction is 2% .

q.6 : During a sale, a shop offered a discount of 10% on th M.P. of all the items. What would a customer have to pay for a pair jeans marked at Rs 1,450 and two shirts marked at Rs 850 each ?

Sol : M.P. of a pair of Jeans = Rs 1,450 M.P. of a Shirt = Rs 850 M.P. of the two Shirts = Rs (2 x 850) = Rs 1,700

T.M.P. of a pair of Jeans and Shirts = Rs 1,450 + Rs

1,700 = Rs 3,150 Discount of 10% = 10/100 x 3,150 = Rs 315 S.P. = T.M.P. – Discount = Rs 3150 – Rs 315 = Rs 2835 Therefore, the customer will have to

pay Rs 20,000 each for a pair of jeans

and two shirts .

q.7 : A milkman sold two of his buffaloes for Rs 20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss ?

Sol : C.P. of both the two buffaloes be (x)

and (y) . S.P. of each buffalo = Rs 20,000 C.P. of the first buffalo = S.P. x 100/100 + 5 = 20,000 x 100/105 = 4,00,000/21

C.P. of the second buffalo = S.P. x 100/100 – 10 = 20,000 x 100/90 = 2,00,000/9 Over-all loss = C.P. – S.P. = 4,00,000/21 + 2,00,000/9 –

40,000/1 = 12,00,000 + 14,00,000 –

25,20,000/63 = 80,000/63 = Rs 1,269.84

q.8 : The price of a TV is Rs 13,000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it ?

Sol : C.P. of the T.V = Rs 13,000 Sales tax charged on it = 12% of

13,000 = 12/100 x

13,000 = Rs 1,560 S.P. = C.P. + Sales tax = Rs (13,000 + 1,560) = Rs

14,560

q.9 : Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is Rs 1,600, find the marked price ?

Sol : Let the M.P. be Rs (x) . Discount of 20% = 20/100 x

(x) = Rs x/5 S.P. = M.P. – Discount = Rs x – Rs x/5 = Rs 4x/5

According to the question ; 4x/5 = 1,600 x = 1,600 x 5/4 x = Rs 2,000 Therefore, the M.P. of the pair of

skates is Rs 2,000 .

q.10 : I purchased a hair – dryer for Rs 5,400 including 8% VAT. Find the price before VAT was added ?

Sol : When the price including VAT is Rs 108 , Original price = Rs 100 When price including VAT is Rs 5,400

, Original price = Rs 100/108 x

5,400 = Rs 5,000Therefore, the price before VAT was

added is Rs 5,000

Exercise : 8.3q.1 : Calculate the amount and

compound interest on :(a): Rs 10,800 for 3 years at 12 ½

% per annum compounded anually .

Sol : P : Rs 10,800 R : 12 ½ % = 25/2 % T : 3 years

(( )

( ))820

0 3

31n

83

81350

672

88 841

= 675 x 9 x 9 x 9

= 675 x 729

= 4,92,075

= Rs 15,377.34 C.P. = A – P = 15,377.34 –

10,800 = Rs 4,577.34

32

32

8

(b) : Rs 18,000 for 2 ½ year ay 10% per annum compounded annualy .

Sol : P ; Rs 18,000 R : 10% T : 2 ½ year A = P ( 1+R /100 ) = 18,000 1+10

= 18,000 10 + 1 )()(100

n2

2

10

= 18,000 11

= 18,000 x 11 x 11

= 180 x 121 = Rs 21,780

S.I. = PRT = 21,780 x 10 x ½

= Rs 1,089

)(

100

10

10

10

2

C.I. = A – P = 21,780 – 18,000 = Rs 3,80

T.C.I. = 3,780 + 1,089 = Rs 4,869

A of 2 ½ year = P + I = 21,780 + 1,089 = Rs 22,869

(c) : Rs 62,500 for 1 ½ year at 8% per annum compounded half yearly .

Sol : P = Rs 62,500 R = 8% = 4 years T = 1 ½ year = 3 A = P 1 + R

= 62,500 1 + 4

n

)()(

3

100

100

= 62,000 25 + 1

= 62,500 26

= 62,500 x 26 x 26 x 26

= 4 x 26 x 26 x 26 = Rs 70,304

))

((25

25

25 252511 1

1002,5004

3

3

C.I. = A – P = 70,304 – 62,500 Rs 7,804

(d) : Rs 8,000 for 1 year at 9% per annum compounded half yearly .

Sol : P = Rs 8,000 R = 9% = 9/2 T = 1 year A = P 1 + R

= 8,000 1 + 9 ))

((

200

2002

n

= 8,000 200 + 9

= 8,000 209

= 8,000 x 209 x 209

= 2 x 209 x 209

= 47,362

(( )

)200

200

200200

10

10

10 1

2

2

24

= Rs 8,736.2

C.I. = A – P = 8,736.2 – 8,000 = Rs 736.2

(e) : Rs 10,000 for 1 year T 8% per annum compounded half yearly .

Sol : P = Rs 10,000 R = 8% = 4% T = 1 year = 2 A = P 1 + R

= 10,000 1 + 4 ((

))

25

100

100

n

21

= 10,000 25 + 1

= 10,000 26

= 10,000 x 26 x 26

= 16 x 26 x 26

= Rs 10,816

((

))

25

25

2525

10016

2

2

C.I = A – p

= 10,816 – 10,000 = Rs 816

q.2 : Kamala borrowed Rs 26,400 from a bank to buy a scooter at a rate of 15% p.a. compounded annually . What amount will she pay at the end of 2 years and 4 months to clear the loan ?

Sol : P = Rs 26,400 R = 15% T = 2 years, 4 months = 2 y. and 1/3 y. = 2

100

((

((

))

))10

0

20

20

2020

20

3 2

2

2

2

66

132

= 66 x 23 x 23 = Rs 34,914

S.I. = PRT = 34,914 x 15 x 1

= 34,914 x 5

= 1,74,570

= Rs 1,745.70

100

100

100

100 x 3

1

T.A = 34,914 + 1,745.70 = Rs 36,659.70

C.I = A – P = 36,659.70 – 26,400 = Rs 10,259.70

q.3 : Fabina borrows Rs 12,500 at 12% per annum for 3 years at S.I and Radha borrows the same amount for the same time period at 10% per annum , compounded annually . Who pays more interest and by how much ?

Sol : For Fabina ; P = Rs 12,500 R = 12% T = 3 years

S.I = = 12,500 x 12 x 3

= 125 x 12 x 3 = Rs 4,500

For Radha ; P = Rs 12,500 R = 10% T = 3 years

PRT100

100

A = P 1 + R

= 12,500 1 + 10

= 12,500 10 + 1

= 12,500 11

=12,500 x 11 x 11 x 11

((

((

)))

)

10

10

10

10

10

3100

100

3

n

= 125 x 11 x 11 x 11

= 1,66,375

= Rs 1,66,375.50

C.I = A – P = 1,66,375.50 – 12,500.00 = Rs 4,137.50

10

10

Difference between C.I and S.I ; = 4,500.00 – 4,137.50 = Rs 362.50

Therefore , Fabina pays more money by

Rs 362.50 than Radha .

q.4 : I borrowed Rs 12,000 from jamshed at 6% per annum simple interest for 2 years . Had I borrowed this sum at 6% per annum coumpound , what exess amount would I have to pay ?

Sol : P = Rs 12,000 R = 6% T = 2 years S.I = PRT = 12,000 x 6 x 2

= 120 x 12 = Rs 1,440

100

100

((

50

( ))

))

(

100

50

3100

n

2

2

2

24

50

50

1

50

= 24 x 53 x 53

= Rs 13,483.20

C.I = A – P = 13,483.20 – 12,000.00 = Rs 1,483.20

Excess A = 1,483.20 – 1,440.00 = Rs 43.20 Therefore , I would have to pay to

him an excess amoun of Rs 43.20 .

q.5 : Vasudevan invested Rs 60,000 at an interest rate of 12% per annum compouunded half yearly . What amount would he get

(i) After 6 months ?Sol : P = Rs 60,000 R = 12% = 6% T = ½ year = 1 half year

A = P 1 + R

= 60,000 1 + 6

= 60,000 100 + 6

= 60,000 106

= 60,000 x 106

)

(

((( )

)100

100

100

100

n

1

100

1

1

= 600 x 106 = Rs 63,600

There fore , he would get Rs 63,600 after

6 months .

(ii) : After 1 year ?Sol : P = Rs 60,000 R = 12% = 6% T = 1 year = 2 A = P 1 + R

= 60,000 1 + 6

( )n

100 2)( 3

50

100

= 60,000 50 + 3 = 60,000 53 =60,000 x 53 x 53 50 50 = 120 x 53 x 53 = 24 x 53 x 53 = Rs 67,416

1

51

24

( )( )2

2

120

q.6 : Arif took a loan of Rs 80,000 frm a bank . If the rate of interest is 10% per annum , find the difference in amounts he would be paying after 1 ½ years if the interest is ;

(i) : Compounded annually ?Sol : P = Rs 80,000 R = 10% T = 1 ½ year = 1 year

A = P 1 + R

= 80,000 1 + 10

= 80,000 10 + 1

= 80,000 11

= 80,000 x 11

(

(

100

n

(

(

100

1

((

10

1

(10

(1

10

= 8,000 x 11 = Rs 88,000

S.I = PRT = 88,000 x 10 x 1

= Rs 4,400

100

2 x 100

4,400

1

(ii) : Compounded half – yearly ?Sol : P = Rs 80,000 R = 10% = 5% T = 1 ½ years = 3 A = P 1 + R

= 80,000 1 + 5

( )100

n

( 100

)3

20

1

= 80,000 20 + 1

= 80,000 21

= 80,000 x 21 x 21 x 21

= 10 x 21 x 21 x 21 = Rs 92,610

(

(

20

3

(20

(3

20 20 20

40

1

10

1

20

1

q.7 : Maria invested Rs 8,000 in a business. She would be paid interest at rate of 5% per annum compounded annually . Find ;

(i): The amount credit against her name at the end of the second year .

Sol : P = Rs 8,00 R = 5% T = 2 years A = P 1 + R

(

(

100

n

= 8,000 1 + 5

= 8,000 20 + 1

= 8,000 21

= 8,000 x 21 x 21

= 20 x 21 x 21 = Rs 8,820

(

(

100

2

20

1

(

(

20

2

(20

(2

20

20

400

11

20

(ii) : The interest for the third year .Sol : P = Rs 8,820 R = 5% T = 1 years A = P 1 + R

= 8,820 1 + 5

= 8,820 20 + 1

(((

(( (

1

n

1

100

100

20

20

1

= 8,820 21

= 8,820 x 21

= 441 x 21 = Rs 9,261

(

(

20

1

20

441

1

q.8 : Find the amount and the compound interest on Rs 10,000 for 1 ½ years at 10% per annum, compounded half yearly . Would this interest be more than the interest he would get if it was compounded annually ?

Sol : P = Rs 10,000 R = 10% = 5% T = 1 ½ years = 3

Compounded haif - yearly A = P 1 + R

= 10,000 1 + 5

= 10,000 20 + 1

= 10,000 21

( )100

n

( )100

3

20

1

( )20

3

(20)3

= 10,000 x 21 x 21 x 21

= Rs 11,576.25

C.I = A – P = 11,576.25 – 10,000 = Rs 1,576.25

There fore , the interest when compounded half yearly would be more than the interest when compounded annually .

20

20

20

q.9 : Find the amount which Ram will get on Rs 4,096 , if he gave it for 18 months at 12 ½ years per annum , interest being compounded half - yearly ?

Sol : P = Rs 4,096 R = 12 ½ % = 25/2% =1/2 x 25/2% = 25/4% T = 18 months = 3 A = P 1 + R

( )100

n

= 4,096 1 + 25

= 4,096 1 + 25

= 4,096 16 + 1

= 4,096 17

= 4,096 x 17 x 17 x 17

( 4 x 100

)3

( 400

)3

(16

1

)3

16(1

6

)3

16

16

16

= Rs 4,913

There fore , the required amount is

Rs 4,913 .

Muliple choise

question

q.1 : The fraction 2/5 converted to % age is:

(a) : 20% (c) : 40% (b) : 30% (d) : 50%

Q.2 : The marked price of a book is Rs 100 . The shopkeeper give 25% discount on it . What is the sale price of the book ?

(a) : Rs 100 (c) : Rs 25 (b0 : Rs 125 (d) : Rs 75

Q.3 : A toy marked at Rs 40 is available for Rs 32 . What % discount is given on the marked price ?

(a) : 10% (c) : 25% (b) : 20% (d) : 40%

Q.4 : Meenu purchased a fridge for Rs 10,000 and sold it for Rs 8,000 . Find her loss .

(a) Rs 8,000 (c) : Rs 2,000 (b) : Rs 10,000 (d) : Rs

12,000

Q.5 : Saroj purchased a watch for Rs 1,000 and she sold it for Rs 1,200 . What is her profit ?

(a) : Rs 1,000 (c) : Rs 200 (b) : Rs 1,200 (d) : Rs 800

Q.6 : Kanti purchased a sewing machine for Rs 2,000 . She sold it at a loss of 40% . Find the selling price .

(a) : Rs 1,200 (c) : Rs 800 ( b) : Rs 400 (d) : Rs 2,800

Q.7 : Rani purchased a T.V for Rs 10,000 and sold it for Rs 8,000 . Find her loss % .

(a) : 10% (c) : 40% (b) : 20% (d) : 60%

Q.8 : Sapna purchased a cycle for Rs 1,000 and sold it for Rs 1,200 . Find her gain %.

(a) : 20% (c) : 40% (b) : 10% (d) : 12%

Q.9 : Find the simple interest on Rs 1,000 for 2 years at 8% per annum .

(a) : Rs 80 (c) : Rs 120 (b) : Rs 40 (d) : Rs 160

Q.10 : A sofa set was brought for rs 10,000. Its value depreciated at the rate of 10% per annum. Find its value after one year .

(a) : Rs 11,000 (c) : Rs 10,000

(b) : Rs 9,000 (d) : Rs 1,000

Q.11 : There are 1,275 trees in Chaudary Farm. Out of these 36% trees are of fruits. How many trees of fruits are there in Chaudary Farm ?

(a) : 459 (c) : 549 (b) : 945 (d) : 954

Q.12 : The salary of Manish is Rs 10,000. His salary gets increased by 10% . Find his increased salary .

(a) : Rs 9,000 (c) : Rs 8,000 (b) : Rs 11,000 (d) : Rs 12,000

Q.13 : The simple interest 0n Rs 2,000 for 4 years is Rs 400 . The rate % of interest is :

(a) : 2,000 x 100/400 x 4 (b) : 400 x 4/2,000 x 100 (c) : 400 x 100/2,000 x 4 (d) : 2,000 x 4/400 x 100

Q.14 : a sum is taken for one year at 9% p.a. If interest is compounded after every three months, how many times will interest charged in one year ?

(a) : 2 times (c) : 4 times

(b) : 3 times (d) : 1 time

Answers are in the next slide :

Solutions :(1) : 40 % (8) : 20% (2) : Rs 75 (9) : Rs 160 (3) : 20% (10) : Rs 9,000(4) : Rs 2,000 (11) : 459 (5) : Rs 200 (12) : Rs 11,000 (6) : Rs 1,200 (13) : 400 x

100/2,000 x 4 (7) : 20% (14) : 4 times