NCERT Solutions for Chapter 8 Comparing Quantities Class 8 Maths
Book Solutions1
Find the ratio of the following:
(a) Speed of a cycle 15 km per hour to the speed of scooter 30 km per hour.
(b) 5 m to 10 km
(c) 50 paise to Rs. 5
Answer
(a) Speed of cycle = 15 km/hr
Speed of scooter = 30 km/hr
Hence ratio of speed of cycle to that of scooter = 15 : 30 = 15/30 = 1/2= 1 : 2
(b) ∵ 1 km = 1000 m
∴ 10 km = 10×1000 = 10000 m
∴ Ratio = 5m/10000m = 1/2000 = 1 : 2000
(c) ∵ Rs 1 = 100 paise
∴ Rs 5 = 5× 100 = 500 paise
Hence Ratio = 50 paise/ 500 paise = 1/10 = 1 : 10
2
Convert the following ratios to percentages:
(a) 3 : 4
(b) 2 : 3
Answer
(a) Percentage of 3 : 4 = 3/4 ×100 % = 75%
(b) Percentage of 2 : 3 = 2/3 × 100% = 66.2/3%
3
Answer
Total number of students = 25
Number of good students in mathematics = 72% of 25 = 72/100 ×25 = 18
Number of students not good in mathematics = 25 – 18 = 7
Hence percentage of students not good in mathematics = 7/25 × 100 = 28%
4
Answer
Let total number of matches be x.
According to question,
40% of total matches = 10
⇒ 40% of x = 10
⇒ 40/100 × x = 10
⇒ x = (10×100)/40 = 25
Hence total number of matches are 25.
5
Answer
Total percentage of money she didn't spent = 100% - 75%=25%
According to question,
⇒ 25% = 600
⇒ 1% = 600/25
⇒ 100% = 600/ 25 × 100
Hence the money in the beginning was Rs 2,400.
6
Answer
Number of people who like cricket = 60%
Number of people who like football = 30%
Number of people who like other games = 100% – (60% + 30%) = 10%
Now Number of people who like cricket = 60% of 50,00,000
= 60/100 × 50,00,000 = 30,00,000
And Number of people who like football
= 30% of 50,00,000
= 30/100 × 50,00,000 = 15,00,000
∴ Number of people who like other games = 10% of 50,00,000
= 10/100 × 50,00,000 = 5,00,000
Hence, number of people who like other games are 5 lakh.
1
Answer
Let original salary be Rs.100.
Therefore New salary i.e., 10% increase
= 100 + 10 = Rs.110
∵ New salary is Rs.110, when original salary = Rs.100
∴ New salary is Rs.1, when original salary = 100/110
∴ New salary is Rs.1,54,000, when original salary = 100/110 × 154000 = Rs.1,40,000
Hence original salary is Rs. 1,40,000.
2
Answer
On Sunday, people went to the Zoo = 845
On Monday, people went to the Zoo = 169
Number of decrease in the people = 845 – 169 = 676
Decrease percent = 676/845 × 100 = 80%
Hence decrease in the people visiting the Zoo is 80%.
3
Answer
No. of articles = 80
Cost Price of articles = Rs. 2,400
And Profit = 16%
∵ Cost price of articles is Rs.100, then selling price = 100 + 16 = Rs.116
∴ Cost price of articles is Rs.1, then selling price = 116/100
∴ Cost price of articles is Rs.2400, then selling price = 116/100 × 2400 = Rs.2784
Hence, Selling Price of 80 articles = Rs.2784
Therefore Selling Price of 1 article
= 2784/80 = Rs.34.80
4
Answer
Here, C.P. = Rs.15,500 and Repair cost = Rs.450
Therefore Total Cost Price = 15500 + 450 = Rs.15,950
Let C.P. be Rs.100, then S.P. = 100 + 15 = Rs.115
∵ When C.P. is Rs.100, then S.P. = Rs.115
∴ When C.P. is Rs.1, then S.P. = 115/100
∴ When C.P. is Rs.15950, then S.P.
=115/100 × 15950 = Rs.18,342.50
5
Answer
Cost price of VCR = Rs.8000 and Cost price of TV = Rs.8000
Total Cost Price of both articles
= Rs.8000 + Rs.8000 = Rs. 16,000
Now VCR is sold at 4% loss.
Let C.P. of each article be Rs.100, then S.P. of VCR = 100 – 4 = Rs.96
∴ When C.P. is Rs.100, then S.P. = Rs.96
∴ When C.P. is Rs.1, then S.P. = 96/100
∴ When C.P. is Rs.8000, then S.P.
= 96/100 ×8000 = Rs.7,680
And TV is sold at 8% profit, then S.P. of TV = 100 + 8 = Rs.108
∵ When C.P. is Rs.100, then S.P. = Rs.108
∴ When C.P. is Rs.1, then S.P. = 108/100
∴ When C.P. is Rs.8000, then S.P.
= 108/100 × 8000 = Rs.8,640
Then, Total S.P.
= Rs.7,680 + Rs.8,640 = Rs. 16,320
Since S.P. >C.P.,
Therefore Profit = S.P. – C.P.
= 16320 – 16000 = Rs.320
And Profit% = Profit/ cost price × 100
= 320/16000 × 100 = 2%
Therefore,the shopkeeper had a gain of 2% on the whole transaction.
6
Answer
Rate of discount on all items = 10%
Marked Price of a pair of jeans = Rs.1450 and Marked Price of a shirt = Rs.850
Discount on a pair of jeans
= (Rate × M.P)/100 = (10×1450)/100 = Rs.145
∴ S.P. of a pair of jeans = Rs.1450 – Rs.145 = Rs.1305
Marked Price of two shirts = 2× 850 = Rs.1700
Discount on two shirts = (Rate × M.P)/100 = (10 × 1700)/100 = Rs.170
∴ S.P. of two shirts = Rs.1700 – Rs.170 = Rs.1530
Therefore the customer had to pay = 1305 + 1530
= Discount on a pair of jeans
= (Rate × M.P)/100 = (10×1450)/100
= Rs.145
∴ S.P. of a pair of jeans
= Rs.1450 – Rs.145 = Rs.2,835
Thus,the customer will have to pay Rs.2,835
7
Answer
S.P. of each buffalo = Rs.20,000
S.P. of two buffaloes = 20,000 × 2 = Rs.40,000
One buffalo is sold at 5% gain.
Let C.P. be Rs.100, then S.P. = 100 + 5 = Rs.105
∵ When S.P. is Rs.105, then C.P. = Rs.100
∴ When S.P. is Rs.1, then C.P. = 100/105
∴ When S.P. is Rs.20,000, then C.P.
= 100/105 × 20000 = Rs.19,047.62
Another buffalo is sold at 10% loss.
Let C.P. be Rs.100, then S.P. = 100 – 10 = Rs.90
∵ When S.P. is Rs.90, then C.P. = Rs.100
∴ When S.P. is Rs.1, then C.P. = 100/90
∴ When S.P. is Rs.20,000, then C.P.
= 100/90 × 20000 = Rs.22,222.22
Total C.P. = Rs.19,047.62 + Rs.22,222.22
= Rs.41,269.84
Since C.P. >S.P.
Therefore here it is loss.
Loss = C.P. – S.P.
= Rs.41,269.84 – Rs. 40,000.00 = Rs.1,269.84
The overall loss of milkman was Rs.1269.84
8
Answer
C.P. = Rs.13,000 and S.T. rate = 12%
Let C.P. be Rs.100, then S.P. for purchaser
= 100 + 12 = Rs.112
∵ When C.P. is Rs.100, then S.P. = Rs.112
∴ When C.P. is Rs.1, then S.P. = 112/100
∴ When C.P. is Rs.13,000, then S.P.
= 112/100 × 13000 = Rs.14,560
He will have to pay Rs.14,560
9
Answer
S.P. = Rs.1,600 and Rate of discount = 20%
Let M.P. be Rs.100, then S.P. for customer = 100 – 20 = Rs.80
∵ When S.P. is Rs.80, then M.P. = Rs.100
∴ When S.P. is Rs.1, then M.P. = 100/80
∴ When S.P. is Rs.1600, then M.P.
= 100/ 80 × 1600 = Rs.2,000
Thus, the marked price was Rs. 2,000
10
Answer
C.P. = Rs.5,400 and Rate of VAT = 8%
Let C.P. without VAT is Rs. 100, then price including VAT = 100 + 8 = Rs.108
∵ When price including VAT is Rs.108, then original price = Rs.100
∴ When price including VAT is Rs.1, then original price = 100/108
∴ When price including VAT is Rs.5400, then original price = 100/108 × 5400 = Rs.5000
Thus, the price of Hair Dryer before the addition of VAT was Rs 5000
1
Calculate the amount and compound interest on:
(a) Rs.10,800 for 3 years at 12.1/2% per annum compounded annually.
(b) Rs.18,000 for 2.1/2 years at 10% per annum compounded annually.
(c) Rs.62,500 for 1.1/2 years at 8% per annum compounded annually.
(d) Rs.8,000 for 1 years at 9% per annum compounded half yearly. (You could the year by year calculation using S.I. formula to verify).
(e) Rs.10,000 for 1 years at 8% per annum compounded half yearly.
Answer
(a) Here, Principal (P) = Rs. 10800, Time(n) = 3 years,
Rate of interest (R) = 12.1/2% = 25/2 %
Amount (A) = 
= 
=
= 
= 
= 10800 × 9/8 × 9/8 × 9/8
= Rs. 15,377.34 (approx.)
Compound Interest (C.I.) = A – P
= Rs. 10800 – Rs. 15377.34 = Rs. 4,577.34
(b) Here, Principal (P) = Rs. 18,000, Time (n) = 2.1/2 years, Rate of interest (R)
= 10% p.a.
Amount (A) =
= 
= 
= 18000(11/10)2 = 18000 × 11/10 ×11/10
= Rs. 21,780
Interest for 1/2 years on Rs. 21,780 at rate of 10% = (21780×10×1)/100 = Rs. 1,089
Total amount for 2.1/2 years
= Rs. 21,780 + Rs. 1089 = Rs. 22,869
Compound Interest (C.I.) = A – P
= Rs. 22869 – Rs. 18000 = Rs. 4,869
(c) Here, Principal (P) = Rs. 62500, Time (n) = 1.1/2 = 3/2 years = 3 years (compounded half yearly)
Rate of interest (R) = 8% = 4% (compounded half yearly)
Amount (A) =
= 
= 
= 62500 (26/25)3
= 62500 × 26/25 × 26/25 × 26/25
= Rs. 70,304
Compound Interest (C.I.) = A – P
= Rs. 70304 – Rs. 62500 = Rs. 7,804
(d) Here, Principal (P) = Rs. 8000, Time (n) = 1 years = 2 years(compounded half yearly)
Rate of interest (R) = 9% = 9/2 % (compounded half yearly)
Amount (A) =
= 
= 
= 8000 (209/200)2
= 8000 × 209/200 × 209/200
= Rs. 8,736.20
Compound Interest (C.I.) = A – P
= Rs. 8736.20 – Rs. 8000
= Rs. 736.20
(e) Here, Principal (P) = Rs. 10,000, Time (n) = 1 years = 2 years (compounded half yearly)
Rate of interest (R) = 8% = 4% (compounded half yearly)
Amount (A) =
= 
= 
= 10000 (26/25)2
= 10000 × 26/26 × 26/25
= Rs. 10,816
Compound Interest (C.I.) = A – P
= Rs. 10,816 – Rs. 10,000 = Rs. 816
2
(Hint: Find A for 2 years with interest is compounded yearly and then find SI on the 2nd year amount for 4/12 years).
Answer
Here, Principal (P) = Rs. 26,400, Time(n) = 2 years 4 months, Rate of interest (R) = 15% p.a.
Amount for 2 years (A) =
= 
= 
= 26400(23/20)2 = 26400 × 23/20 × 23/20
= Rs. 34,914
Interest for 4 months = 4/12 = 1/3 years at the rate of 15% = (34914 × 15×1)/100
= Rs. 1745.70
Total amount = Rs. 34,914 + Rs. 1,745.70
= Rs. 36,659.70
3
Answer
Here, Principal (P) = Rs.12,500, Time (T) = 3 years, Rate of interest (R)
= 12% p.a.
Simple Interest for Fabina = 
= 
= Rs. 4,500
Amount for Radha, P = Rs. 12,500, R = 10% and 
= 3 years
Amount (A) = 
= 
= 
= 
= 
= Rs. 16,637.50
C.I. for Radha = A – P
= Rs. 16,637.50 – Rs. 12,500 = Rs. 4,137.50
Thus, Fabina pays more interest
= Rs. 4,500 – Rs. 4,137.50 = Rs. 362.50
4
Answer
Here, Principal (P) = Rs.12,000, Time (T) = 2 years, Rate of interest (R) = 6% p.a.
Simple Interest = (P×R×T)/100
= (12000 × 6× 2)/100 = Rs. 1,440
Had he borrowed this sum at 6% p.a., then
Compound Interest =- P
= 
= 
= 12000(53/50)2 - 12000
= 12000 × 53/50 × 53/50 - 12000
= Rs. 13,483.20 – Rs. 12,000
= Rs. 1,483.20
Difference in both interests
= Rs. 1,483.20 – Rs. 1,440.00 = Rs. 43.20
Thus ,the extra amount to be paid is Rs.43.20
5
(i) after 6 months?
(ii) after 1 year?
Answer
(i) Here, Principal (P) = Rs. 60,000,
Time (n)= 6 months = 1 year(compounded half yearly)
Rate of interest (R) = 12% = 6% (compounded half yearly)
Amount (A) =
= 
= 
= 60000 (53/50)1
= 60000 × 53/50
= Rs. 63,600
After 6 months Vasudevan would get amount Rs. 63,600.
(ii) Here, Principal (P) = Rs. 60,000,
Time (n) = 1 year = 2 year(compounded half yearly)
Rate of interest (R) = 12% = 6% (compounded half yearly)
Amount (A) =
= 
= 
= 60000(53/50)2
= 60000 × 53/50 × 53/50
= Rs. 67,416
After 1 year Vasudevan would get amount Rs. 67,416.
6
(i) compounded annually.
(ii) compounded half yearly.
Answer
(i) Here, Principal (P) = Rs. 80,000, Time (n)= 1.1/2 years, Rate of interest (R) = 10%
Amount for 1 year (A) =
= 
=
= 80000 (11/10)1
= Rs. 88,000
Interest for 1/2 year = (88000×10×1)/(100×2)
= Rs. 4,400
Total amount = Rs. 88,000 + Rs. 4,400 = Rs. 92,400
(ii) Here, Principal (P) = Rs.80,000,
Time (n) = 1.1/2 year = 3/2 years (compounded half yearly)
Rate of interest (R) = 10% = 5% (compounded half yearly)
Amount (A) =
= 
= 
= 80000(21/20)3
= 80000 × 21/20 × 21/20 × 21/20
= Rs. 92,610
Difference in amounts
= Rs. 92,610 – Rs. 92,400 = Rs. 210
7
(i) The amount credited against her name at the end of the second year.
(ii) The interest for the third year.
Answer
(i) Here, Principal (P) = Rs. 8000, Rate of Interest (R) = 5%, Time (n) = 2 years
Amount (A) =
= 
= 
= 8000(21/20)2
= 8000 × 21/20 × 21/20
= Rs. 8,820
(ii) Here, Principal (P) = Rs. 8000, Rate of Interest (R) = 5%, Time (n) = 3 years
Amount (A) =
= 
= 
= 8000(21/20)3
= 8000 × 21/20 × 21/20 × 21/20
= Rs. 9,261
Interest for 3rd year = A – P
= Rs. 9,261 – Rs. 8,820 = Rs. 441
8
Would this interest be more than the interest he would get if it was compounded annually?
Answer
Here, Principal (P) = Rs. 10000, Rate of Interest (R) = 10% = 5% (compounded half yearly)
Time (n) = 1.1/2 years = 3 years (compounded half yearly)
Amount (A) =
= 
= 
= 10000 (21/20)3
= 10000 × 21/20 × 21/20 × 21/20
= Rs. 11,576.25
Compound Interest (C.I.) = A – P
= Rs. 11,576.25 – Rs. 10,000 = Rs. 1,576.25
If it is compounded annually, then
Here, Principal (P) = Rs. 10000, Rate of Interest (R) = 10%, Time (n) = 1.1/2years
Amount (A) for 1 year =
= 
= 
= 10000(11/10)1
= 10000 × 11/10
= Rs. 11,000
Interest for 1/2 year = (11000 × 1 × 10)/(2×100) = Rs. 550
∴ Total amount = Rs. 11,000 + Rs. 550
= Rs. 11,550
Now, C.I. = A – P = Rs. 11,550 – Rs. 10,000
= Rs. 1,550
Yes, interest Rs. 1,576.25 is more than Rs. 1,550.
9
Answer
Here, Principal (P) = Rs. 4096,
Rate of Interest (R) = 12.1/2 = 25/2%
= 25/4% (compounded half yearly)
Time (n)= 18 months = 1.1/2 years = 3 years (compounded half yearly)
Amount (A) =
= 
= 
= 4096(17/16)3
= 4096 × 17/16 × 17/16 × 17/16
= Rs. 4,913
10
(i) Find the population in 2001.
(ii) What would be its population in 2005?
Answer
(i) Here, A2003 = Rs. 54,000, R = 5%, n = 2 years
Population would be less in 2001 than 2003 in two years.
Here population is increasing.
∴ A2003 = 
⇒ 54000 = 
⇒ 54000 = 
⇒ 54000 = P2001 (21/20)2
⇒ 54000 = P2001 ×21/20 × 21/20
⇒ P2001 = (54000 × 20 × 20)/(21 × 21)
=48,979.5
⇒ P2001 =48,980 (approx.)
(ii) According to question, population is increasing. Therefore population in 2005,
A2005 =
= 54000 (1 + 5/100)2
= 54000(1+1/20)2
= 54000(21/20)2
= 54000 × 21/20 × 21/20
= 59,535
Hence population in 2005 would be 59,535.
11
Answer
Here, Principal (P) = 5,06,000, Rate of Interest (R) = 2.5%, Time (n) = 2 hours
After 2 hours, number of bacteria,
Amount (A) =
= 506000(1+ 2.5/100)2
= 506000(1+25/1000)2
= 506000(1+1/40)2
= 506000(41/40)2
= 506000 × 41/40 × 41/40
= 5,31,616.25
Hence, number of bacteria after two hours are 531616 (approx.).
12
Answer
Here, Principal (P) = Rs. 42,000, Rate of Interest (R) = 8%, Time (n) = 1 years
Amount (A) = P ( 1 - R/100)n
= 42000(1 - 8/100)1
= 42000(1+ 2/25)1
= 42000 (27/25)1
= 42000 × 27/25
= Rs. 38,640
Hence, the value of scooter after one year is Rs. 38,640.