Class_VIII_Mathematics(Comparing quantities)

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Chapter : 8
Comparing 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
(b) :
Sol : 2 : 3 % = 2/3
= 2/3 x 100
= 66 2/3 %
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 : 8.2
Q.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 5,000
Therefore, the price before VAT was added
is Rs 5,000
Exercise : 8.3
q.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
A = P ( 1+R /200 ) n
1 3
= 10,000 1 + 25
2008
( )
( )
()
= 10,000 8 + 1
8
= 10,000 9
8
672
1350
3
3
= 10,000 x 9 x 9 x 9
8
8
8
4
1
= 675 x 9 x 9 x 9
8
= 675 x 729
32
= 4,92,075
32
= Rs 15,377.34
C.P. = A – P = 15,377.34 – 10,800
= Rs 4,577.34
(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 ) n
2
= 18,000 1+10
100
( )
( )
= 18,000 10 + 1
10
2
2
()
= 18,000 11
10
= 18,000 x 11 x 11
10 10
= 180 x 121
= Rs 21,780
S.I. = PRT = 21,780 x 10 x ½
100
= Rs 1,089
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
n
A=P 1+R
100
( )
( )
= 62,500 1 + 4
100
3
( )
()
= 62,000 25 + 1
25
= 62,500
4 100
2,500
3
26
25
3
= 62,500 x 26 x 26 x 26
25 25 25
1
1
= 4 x 26 x 26 x 26
= Rs 70,304
1
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
n
A=P 1+R
200
( )
( )
= 8,000 1 + 9
200
2
( )
( )
= 8,000 200 + 9
200
= 8,000
42
2
2
209
200
= 8,000 x 209 x 209
200
200
10
1
= 2 x 209 x 209
10
= 47,362
10
= 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
n
A=P 1+R
100
( )
( )
1
= 10,000 1 + 4
25100
2
( )
( )
= 10,000 25 + 1
25
= 10,000
16
100
26 2
25
= 10,000 x 26 x 26
25 25
= 16 x 26 x 26
= Rs 10,816
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
2
( )
( )
( )
()
A = P 1+ R
100
3
= 26,400 1+15
100
20
= 26,400 20+3
20
= 26,400 23
20
132
2
2
2
66
= 26,400 x 23 x 23
20 20
= 66 x 23 x 23
= Rs 34,914
S.I. = PRT = 34,914 x 15 x 1
100
100 x 3
= 34,914 x 5
100
= 1,74,570
100
= Rs 1,745.70
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 = PRT = 12,500 x 12 x 3
100
100
= 125 x 12 x 3
= Rs 4,500
For Radha ;
P = Rs 12,500
R = 10%
T = 3 years
A=P
n
( )
( )
( )
()
1+R
100
= 12,500 1 + 10
100
= 12,500 10 + 1
10
= 12,500 11
10
3
3
=12,500 x 11 x 11 x 11
10 10 10
= 125 x 11 x 11 x 11
10
= 1,66,375
10
= Rs 1,66,375.50
C.I = A – P
= 1,66,375.50 – 12,500.00
= Rs 4,137.50
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
100
100
= 120 x 12
= Rs 1,440
A=P
n
( )
( )
( )
()
1+R
100
3 2
= 12,500 1 + 6
100
50
= 12,500 50 + 3
50
= 12,500
24
53
50
2
= 12,500 x 53 x 53
50 1 50
2
= 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
100
n
1
( )
( )
()
= 60,000 1 + 6
100
1
= 60,000 100 + 6
100
= 60,000 106 1
100
= 60,000 x 106
100
= 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
n
A=P 1+R
100
( )
( )
3
= 60,000 1 + 6
100
50
2
( )
()
= 60,000 50 + 3
= 60,000
120
2
53
2
=60,000 x 53 x 53
50
50
1
24
= 120 x 53 x 53
5
1
= 24 x 53 x 53
= Rs 67,416
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
(
(
(
(
(
(
1+R
100
(
A=P
n
= 80,000 1 + 10
100
= 80,000 10 + 1
10
= 80,000 x 11
10
(
= 80,000 11
10
1
1
1
= 8,000 x 11
= Rs 88,000
4,400
S.I = PRT = 88,000 x 10 x 1
100
2
x
100
1
= Rs 4,400
(ii) : Compounded half – yearly ?
Sol : P = Rs 80,000
R = 10% = 5%
T = 1 ½ years
=3
n
A=P 1+R
( )
( )
100
1
= 80,000 1 + 5
100
20
3
(
(
(
= 80,000 20 + 1
20
40
3
(
= 80,000 21
20
10
20
3
= 80,000 x 21 x 21 x 21
1 20 1 20 1 20
= 10 x 21 x 21 x 21
= Rs 92,610
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
n
A=P 1+R
100
(
(
(
(
= 8,000 1 +15 2
100
(
(
(
20
= 8,000 20 + 1
20
2
(
= 8,000 21
20
20
400
2
= 8,000 x 21 x 21
1 20 1 20
= 20 x 21 x 21
= Rs 8,820
(ii) : The interest for the third year .
Sol : P = Rs 8,820
R = 5%
T = 1 years
n
A=P 1+R
100
(
(
= 8,820 1 + 5
100
20
1
(
(
(
(
1
= 8,820 20 + 1
20
1
(
(
= 8,820 21
20
441
1
= 8,820 x 21
1 20
= 441 x 21
= Rs 9,261
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
n
A=P 1+R
100
( )
( )
( )
()
= 10,000
1
1+5
100
20
= 10,000 20 + 1
20
= 10,000
21
20
3
3
3
= 10,000 x 21 x 21 x 21
20 20 20
= 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 .
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
n
A=P 1+R
100
( )
= 4,096 1 + 25 3
4 x 100
( )
( )
( )
( )
1
= 4,096 1 + 25 3
400
16
= 4,096 16 + 1 3
16
= 4,096 17 3
16
= 4,096 x 17 x 17 x 17
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 %
(2) : Rs 75
(3) : 20%
(4) : Rs 2,000
(5) : Rs 200
(6) : Rs 1,200
(7) : 20%
(8) : 20%
(9) : Rs 160
(10) : Rs 9,000
(11) : 459
(12) : Rs 11,000
(13) : 400 x 100/2,000 x 4
(14) : 4 times
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