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BOOK 8 ( CBSE ) / Chap8/ Comparing Quantities.
Chapter Facts.
Some Important Terms
CP : The price at which an article is bought. It includes overheads.
SP : Selling price: The price at which an article is sold. It includes the listed price and
sales tax.
MP : marked price : The price marked or written on an item on sale ( MP is also called
list price or LP )
Discount : The reduction made on the marked price of the item. If no discount is given
then selling price is same as marked price.
ST : Sales tax : Tax to be paid to the government on the sale of a particular item. It is
calculated as a given percentage of list price.
CI : Compound Interest : - Money is said to be at compound interest if at the end of the
year or a fixed period the interest that becomes due is not paid but added to the principal
and the amount obtained becomes the new principal. The process is repeated till the
amount for the last period is determined. Now the difference between the final amount
and the principal is called compound interest. It is always more than the simple interest
provided principal , rate and time are same.
Appreciation : Increase in price or quantity with the passage of time is called
appreciation. Appreciated value is always more than the original value.
Depreciation : Decrease in price or quantity with the passage of time is called
depreciation. Depreciated value is always less than the original value.
1. Per cent means per hundred. It is a way to compare quantities.
2. To write a decimal as a percent we multiply the decimal by 100.
3. To write a percent as a decimal we drop the % symbol and divide the number by 100.
4. To write a fraction as percent we multiply the fraction by 100, simplify and attach the
symbol of %.
5. To write a percent as a fraction we drop the % symbol and divide the number by 100.
6. To convert ratio to percentage we first write it as a fraction and then convert the
fraction to percentage.
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a
100
7. a% of n =
n
100
.
a
8. Suppose a% of x is b , then x = b 
9. Percentage decrease =
decrease in quantiy
100%
original quantity
10. Percentage increase =
increase in quantiy
100%
original quantity
11. To decrease a number by a % multiply it by
100  a
.
100
12. To increase a number by a % multiply it by
100  a
100
13. SP > CP  profit or gain
Profit = SP – CP
profit % =
SP  CP
100%
CP
or
Pr ofit
100%
CP
14. If profit is P % then ,
Profit =
100
100  P  CP
P
SP .
x CP , SP =
and CP =
100  P 
100
100
15. SP < CP  loss
Loss = CP – SP
Loss % =
CP  SP
100% or
CP
loss
100%
CP
16. If loss is L % then,
Loss =
100
100  L  CP
L
SP .
x CP , SP =
and CP =
100  L 
100
100
17. Discount = MP – SP , SP = MP – discount and MP = SP + discount.
18. If discount given is D% then
SP =
100  D
100
MP  SP
MP , MP =
SP and D % =
100%
100
100  D
MP
19. SP = LP + ST ,
LP = SP – ST &
ST = SP – LP.
20. If the rate of sales tax is r % then
ST =
r
100  r
LP , Amount = LP + ST =
LP
100
100
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r 

21. A = P 1 

100


n
, CI = A – P
P : principal , r : effective rate , n : number of conversion periods , A : amount
22. Interest is generally compounded annually, half yearly or quarterly.
Half yearly is also referred to as six monthly or semiannually.
23. Rate of interest is always expressed as per annum.
24. If interest is compounded annually then the effective rate is same as annual rate and
the number of conversion periods is same a number of years.
25. If interest is compounded half yearly then the effective rate : r =
annual rate
and
2
the number of conversion periods :n = ( time in years ) x 2
Note: If time is 1 year then n = 2 , if time is 1½ years then n = 3 etc.
26. If interest is paid per annum and time is in fraction of an year , say a
b
years then
c
b


a
r 
r  

c

A  P 1 
 1
100  
100 





27. Some important terms : 28. For appreciation
For depreciation
r 

A = P 1 

100




A = P 1 
n
r 

100 
, net increase = A – P
n
, net decrease = P – A .
P : original value :
r : rate of Appreciation and Depreciation
n : number of conversion periods
A : final value
Formative Assessment
A ) Multiple choice questions
Tick () the correct option for each of the following :
1. The ratio of 50 piase to Rs 3 is
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(a) 50 : 3
2.
(b) 3 : 50
(c) 6 : 1
(d) 1 : 6
(b) 40
(c) 400
(d) 80
1
% of Rs 8000 is
2
(a) 200
3. An item marked at Rs 9000 is offered in a sale for Rs 8550. The discount percent is
(a) 5%
(b) 6%
(c) 8%
(d) 8
1
%
3
4. The sale price of an item marked at Rs 1275 and sold at 20% discount is
(a) Rs 1020
(b) Rs 680
(c) Rs 1062
(d) Rs 1000
5. Sonia bought an article for Rs 4200 including a tax of 5 %. The price of the article before
VAT was added is
(a) Rs 4100
(b) Rs 3800
(c) Rs 3990
(d) Rs 4000
6. By selling a shirt for Rs 418, a shopkeeper gains 10%. The cost price of the shirt is
(a) Rs 376.2
(b) Rs 380
(c) Rs 372
(d) Rs 408
7. 845 persons visited a monument on Sunday while only 169 people visited it on Monday.
The percent decrease in the visitors is
(a) 60%
(b) 80%
(c) 40%
(d) 50%
8. The compound interest on Rs 8,000 at 5% per annum for 2 years, compounded annually is
(a) Rs 8,820
9.
(b) Rs 400
(c) Rs 820
(d) Rs 1261
The difference between compound interest and simple interest on a sum of Rs 3,000 for 3
years is Rs 93. The rate percent annum is
(a) 8%
(b) 10%
(c) 12%
(d) 15%
10. 45% of the total number of students of a class are girls. If the number of girls is 27, the total
number of students are
(a) 40
(b) 50
(c) 60
(d) 45
11. Out of 250 students , 60% like mathematics. The number of students who do not like
mathematics are
(a) 50
(b) 150
(c) 100
(d) 75
12. The marked price of an item sold at Rs 5225 after allowing a discount of 5% is
(a) Rs 5500
(b) Rs 4963.75
(c) Rs 5486.25
(d) Rs 5000
13. A cycle is bought for Rs 1400, and Rs 100 are paid as transportation charges . If a profit of
5% is made on the cycle, its selling price is
(a) Rs 1525
(b) Rs 1570
(c) Rs 1575
(d) Rs 1625
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14.
Two successive discounts of 20% and 15% are equivalent to a single discount of
(a) 68%
(b) 30%
(c) 35%
(d) 32%
15. When the interest is compounded half yearly, R is rate of interest, P is principal and n is
number of years, then the amount received is given by
R

(a) P  1  
100

2n
R

(b) P  1 
200


n
n
R
R


(c) P  1   (d) P  1 
100
200



2n
.
B ) Fill in the blanks:
1. The amount for which an article is sold is called its _____________ whereas the amount
for which it is bought is called its _____________ .
2. When SP of an article is greater than its CP, there is a _____________ whereas it is a
_____________ if SP is less than CP.
3. The grain or loss is always calculated on the _____________.
4. Additional amount spend on an item before selling it is called _____________.
5. The reduction given on marked price is called _____________.
6. By adding discount to the selling price of an item, we obtain its _____________ .
7. The additional amount charged on the sale of an item by the government is called
_____________.
8. If interest is compounded half- yearly for ‘k’ years , the number of __________ periods is
‘2k’.
C) True / False
Say true or false for each of the following.
1. Reduction given on marked price is called the sales tax.
T/ F .
2. Overhead expenses are included in the cost price before calculating profit
or loss.
T/ F
3. Profit percent is calculated on CP while loss percent is calculated on SP.
T/ F
4. If the interest is compounded half–yearly, then the rate of interest R% per year
changes to
R
% per half year.
2
T/ F
5. If CI and SI are the compound interest and simple interest respectively on a sum P
for n years at the rate of R% pa, then CI is always greater than SI.
T/ F
6. The interest when compounded half yearly is less than the interest compounded
yearly on the same amount for the same period at the same rate.
T/ F
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7. Compound interest is the interest calculated on the previous year’s amount.
T/ F
8. Three and a half years have 7 conversion periods when the interest is compounded
half yearly.
T/ F
D ) True / False with Justification :
Say true or false for each of the following. Justify your answer ?
1. The amount of profit is always less than the CP.
T/ F
2. The amount of discount is always less than the MP.
T/ F
E ) Matching
1. Match the items in column I with those in column II.
Column I
(i)
Percentage form of 3/4
(ii)
Percentage decrease if price reduces
Column II
A 10 %
B 6%
(iii)
from Rs 60 to Rs 54
Percentage increase in price if price
C
75%
(iv)
(v)
(vi)
increases from Rs 50 to Rs 60
Profit percent when SP = 100, CP = 80
Loss percent when SP = 82, CP = 100
Discount percent when SP = 85, MP =
D
E
F
20 %
7%
15 %
(vii)
100
Tax rate when basic price = 200, price
G
8%
(viii
after tax = 214
Gain percent when SP = Rs 200, Gain
H
25%
)
= Rs 12
……
Summative Assessment
A ) One mark questions
1. An item marked at Rs 1,500 is offered in a sale at a discount of 10%. How much does
the customer pay to buy it?
2. A fan is sold Rs. 1,615 after allowing a discount of 5% on the marked price . Find the marked
price.
3. A refrigerator is marked for Rs. 12,000 and is sold for Rs. 10,200. Find the discount percent.
4. What discount percent is offered in a sale if the banner reads “ buy 3 get 2 free” ?
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5. A pen is marked for Rs. 65. If rate of S.T. is 7%. What amount a customer has to pay for it?
6. Marked price of a pair of shoes is Rs. 900. A customer paid Rs. 54 as S.T. for it. What is
the rate of S.T.?
7. After giving a discount of 5% an item is sold for Rs 190. What was its marked price?
8. If interest is compounded semiannually @ 12 % per annum , what is the effective rate ?
9. If interest is compounded semiannually for 18 months, what is the number of conversion
periods?
10. A sum compounded annually becomes121/100 times of itself in 2 years. Determine
the rate of interest per annum.
B ) Two mark questions
1. A retailer marks an article 20% above the cost price of Rs. 800 and allows a discount of 10%.
Find the sale price and the gain percent.
2. An item marked at Rs. 550 is offered in a sale at discount of 20%. If the rate of sales tax is 7%,
find the amount a customer has to pay to purchase it.
3. A fruit seller buys oranges at 3 for Rs. 10 and sells them at 5 for Rs. 20 Find the gain percent.
4. A cycle is sold at a gain of 10%. Had it been sold for Rs. 50 more, the gain would have been
12%. Find its cost price.
5. Shopkeeper purchased a bed for Rs. 7,000. He spent Rs. 300 on its transportation and Rs. 200
on its polishing. He was able to sell it for Rs. 8,100. What was his profit or loss% ?
6. A vendor bought an old T.V. He spent Rs. 200 on transportation and Rs. 1,600 on repairs.
Due to lack of demand he had to sell it for Rs. 1,962. thereby losing 10% in the deal. What price
did he pay to buy the T.V. ?
7. A shop announces a 40% clearance sale. Find the cost price and sale price of an item marked at
Rs. 900 if the shopkeeper loses 10%.
8. Find the amount of Rs. 10,000 for 2 years at 15% per annum compound interest.
9. Find the amount on Rs. 10,000 compounded half yearly for 1 year at the rate of 10% pa.
10. Find the compound interest on Rs. 8,000 compounded half yearly for 1 1 2 years
at the rate of 10% pa.
11. The cost of a generator is Rs. 1,60,000. If its value deprecation at the rate of 5% pa, what will
be its value after 2 years?
12. Value of an car decrease at the rate of 5% every year. If its value is Rs. 2,05,770 at end of
3 years, what was its original value ?
13. Population of town was 3,60,000 in 2004. In 2005 it grew by 4%. In 2006 it dropped by 5%.
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In 2007 it again increased by 10%. What is the population in 2007?
C ) Three mark questions
1. A customer paid Rs. 16,800 to purchase a colour T.V. If this includes tax @ 12% determine the
marked price of the T.V. What will be the new selling price if the rate of S.T. changes to 10%.
2. A farmer borrowed Rs. 10,000 form a money-lender to install a jet pump. The rate of interest is
10% per annum compounded annually. At the end of 3 years the farmer cleared the loan by
paying Rs. 8,000 and a gold ring. Find the cost of the ring.
3. What sum invested for 2 years at the rate of 10% pa compounded annually will amount to
Rs. 2420 ? Also find the interest received.
4. In how many years will a sum of Rs. 25,000 amount to Rs. 28,090 at the rate of 6% pa
compounded annually ?
5. At what rate of interest pa compounded annually will a sum of Rs. 1,250 amount to Rs. 1,458
in 2 years ?
6. What sum invested for 3 years at the rate of 10% pa compounded annually will amount to Rs.
2,662 ? Also find the interest received .
7. In how many years will a sum of Rs. 50,000 yield a compound interest of Rs. 16,550 at the rate
of 10% pa compound annually ?
8. At what rate pa compounded annually will a sum of Rs. 2,50,000 yield a compound interest of
Rs. 47,754 in 3 years ?
9. Harry borrowed Rs. 80,000 at 10% per annum simple interest and lent it to Jai at 10% per
annum compound interest. What will be his gain after 3 years ?
10. What sum invested for 1 year at the rate of 4% pa compounded semi-annually will amount to
Rs. 20,808 ? Also find the interest received.
11. In how many years will a sum of Rs, 30,000 amount to Rs. 31,827 at the rate of 6% pa
compounded six-monthly ?
12. At what rate pa compounded half yearly will a sum of Rs. 5,000 amount to Rs. 5,408 in
1 years.
13. What sum invested for 1 1 2 years at the rate of 8% pa compounded semi-annually
will amount to Rs. 17,576 ?
14. At what rate pa compounded half yearly will a sum of Rs. 20,000 amount to Rs. 26,620
in 1 1 2 years ?
15. In how many years will a sum of Rs. 46,875 yield a compound interest of Rs. 5,853 at the rate
of 8% pa compounded six-monthly ?
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16. Population of a city increases at the rate of 5% pa. If the population in 2010 was 1,76,400,
find the population in 2008 and 2112.
17. A library had 5,120 registered members. The membership increased at the rate of 12.5%
every six months. After what time will the total membership be 7,290?
18. Production of a factory increased from 10,000 units to 13,310 units in three years. Find the
annual rate of growth.
D ) Four mark questions
1. Anil sells two items for Rs. 9,900 each. On one he gains 10% and on the other he loses
10%. Find his gain or loss percent.
2. A fruit seller bought 80 kg apples at Rs. 50 per kg. He sold 70% of the apples at Rs. 60 per kg
and remaining at Rs. 35 per kg. Find his profit or loss?
3. A shopkeeper purchased 100 blankets @ Rs. 2000 each. He found that 10 blankets were
defective an sold them at Rs. 1400 each. At what rat should be sell the remaining blankets s as to
gain 15% on the whole.
4. A coat is marketed in a shop for Rs. 1,284, Rate of S.T. is 7%. A customer tells the shopkeeper
to lower the rate to an extend that he has to pay nothing more than Rs. 1,284 including S.T. Find
the reduction required.
5. Find the difference between compound interest on Rs. 16,000 for 1 1 2 years at 10% pa when
compound annually and when compound compounded semiannually.
End
ANSWERS
Formative
MCQ’s
1
d
2
6
b
7
11
c
12
Fill in the blanks
b
b
a
3
8
13
a
c
c
4
9
14
a
b
d
5
10
15
d
c
d
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1
SP , CP
3
CP
5
discount
7
sales tax
True False
1
F
2
T
6
F
7
T
True False with Justification.
3
8
2
4
6
8
profit , loss
overheads
marked price
conversion
F
T
4
T
5
F
1
F ; Profit has no relation with CP.
2
Suppose CP = Rs 100. Then profit may be any amount. Even more than Rs 100.
T ; If discount = MP , the selling price would be 0. Hence discount cannot
exceed MP.
Matching
(i) – C , (ii) – A, (iii) – D, (iv) – H, (v) - G, (vi) – F, (vii) – E, (viii) – B.
Summative
One mark questions
1
3
5
7
9
Rs 1350
15%
Rs 69.55
Rs 200
3
2
4
6
8
10
Rs 1700
40%
6%
6%
10%
1
Rs 864 , 8%
3
20%
5
8% profit
7
CP = Rs 600, SP = Rs 540
9
Rs 11,025
11
1 year
13
391248
Three marks questions
2
4
6
8
10
12
Rs 470.80
Rs 2,500
Rs 380
Rs 13,225
Rs 1261
Rs 2,40,000
1
3
5
7
9
11
2
4
6
8
10
12
Rs 5,310
2 yrs
Rs 2,000 ; Rs 662
6%
Rs 20,000 ; Rs 808
4%
Two marks questions
Rs 16,500
Rs 2,000 ; Rs 420
8%
3 yrs
Rs 2,480
1 year
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13
Rs 15,625
15
1 ½ years
17
1 ½ years
Four marks questions
14
16
18
20%
194481
10%
1
3
5
2
4
5 % profit
Rs 84
1 % loss
Rs 2,400
Rs 496
END.
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