8 Math Comparing Quantities
8 Math Comparing Quantities
8 Math Comparing Quantities
Comparing Quantities
1. Discount is a reduction given on marked price.
Discount = Marked Price – Sale Price.
3. Additional expenses made after buying an article are included in the cost price and
are known as overhead expenses.
CP = Buying price + Overhead expenses
4. Sales tax is charged on the sale of an item by the government and is added to the
Bill Amount.
Sales tax = Tax% of Bill Amount
R t
A=P(1+ )
200
Where t is number of half years.
Exercise 1
15 1
Answer: Required Ratio = = =1:2
30 2
(b) 5 m to 10 km
5 1
Answer: Required Ratio = = =1:2
10 2
(c) 50 paise to Rs 5
50 1
Ratio = = =1:10
500 10
2. Convert the following ratios to percentages.
(a) 3 : 4
3
Answer: 3:4 =
4
3
On multiplying by 100 you get: × 100 = 75%
4
(b) 2 : 3
2
Answer: 2:3=
3
2 2
On multiplying by 100 you get: × 100 = 66 %
3 3
3. 72% of 25 students are good in mathematics. How many are not good in
mathematics?
4. A football team won 10 matches out of the total number of matches they
played. If their win percentage was 40, then how many matches did they
play in all?
Alternate method:
When the team won 40 matches, number of total match is 100
100
∴ When the team won 1 match, number of total match is
40
100
∴ When the team won 10 matches, number of total match is × 10 = 25
40
5. If Chameli had Rs 600 left after spending 75% of her money, how much
did she have in the beginning?
6. If 60% people in a city like cricket, 30% like football and the remaining
like other games, then what per cent of the people like other games? If the
total number of people are 50 lakh, find the exact number who like each
type of game.
60
Number of Cricket Fans = 50,00,000 × = 30,00,000
100
30
Number of Football Fans = 50,00,000 × = 15,00,000
100
10
Number of Other Sports Fans = 50,00,000 × = 5,00,000
100
Exercise 2
1. A man got a 10% increase in his salary. If his new salary is Rs 1,54,000,
find his original salary.
Alternate Method:
The question can be solved by assuming x for initial salary, as follows:
110
x× = 154000
100
100
⇒ x = 154000 × = 140000
110
2. On Sunday 845 people went to the Zoo. On Monday only 169 people went.
What is the per cent decrease in the people visiting the Zoo on Monday?
Alternate method:
When original number of visitors is 845, the decrease is 676
676
∴ When original number of visitors is 1, the decrease is
845
676
∴ When original number of visitors is 100, the decrease is × 100 = 80%
845
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.
2784
SP of one article = = 34.80
80
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.
Answer: CP=Cost+Overheads
=15500+450=15950
Profit = CP × % profit
15
= 15950 × = 2392.50
100
So, SP = CP+Profit
=15950+2392.50=18342.50
5. A VCR and TV were bought for Rs 8,000 each. The shopkeeper made a
loss of 4% on the VCR and a profit of 8% on the TV. Find the gain or loss
percent on the whole transaction.
Pr ofit
Percentage Profit = × 100
CP
320
= × 100 = 2%
16000
6. During a sale, a shop offered a discount of 10% on the marked prices of
all the items. What would a customer have to pay for a pair of jeans marked
at Rs 1450 and two shirts marked at Rs 850 each?
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.
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.
100
Answer: Marked Price = × FinalPr ice
100 − Discount
100 100
= × 1600 = × 1600 = 2000
100 − 20 80
Alternate Method:
When final price is 80, then marked price is 100
100
∴ When final price is 1, then marked price is
80
100
∴ When final price is 1600, then marked price is = × 1600 = 2000
80
10. I purchased a hair-dryer for Rs 5,400 including 8% VAT. Find the price
before VAT was added.
100
Answer: Price Before VAT = × Final Pr ice
100 + VAT
100
= × 5400 = 5000
108
Exercise 3
R t
Answer: A= P(1+ )
100
1
P = 10800, R= 12 % and t=3 years
2
25
So, A= 10800(1+ )³
200
1
=10800(1+ )³
8
9
=10800( )³
8
9 9 9
= 10800 × × × =15377.34
8 8 8
So, Interest = A-P
=15377.54-10800=4577.34
1
(b) Rs 18,000 for 2 years at 10% per annum compounded annually.
2
10
Answer: Amount = 18000(1+ )²
100
11 11
= 18000 × ×
10 10
=21780
Interest after 2 years = 21780-18000=3780
10 × 1
Plus the interest after half year = 21780 × )=1089
100 × 2
Total interest after 2.5 years = 3780+1089=4869
(c) Rs 62,500 for 1.5 years at 8% per annum compounded half yearly.
26 26 26
= 62500 × × × =70304
25 25 25
So, Interest = 70304-62500=7804
9
Answer: A= 8000(1+ )²
200
209 209
= 8000 × × =8736.20
200 200
So, interest =8736.20-8000=736.20
4
Answer: A=10000(1+ )²
100
26 26
= 10000 × × = 10816
25 25
So, interest = 10816-10000
Alternate method:
Calculating big multiplication can be tedious. Compound interest can also be calcu-
lated by finding yearly amount for each year separately.
Conventional Method
15
A=26400(1+ )²
100
23 23
= 26400 × × = 34914
20 20
3. Fabina borrows Rs 12,500 at 12% per annum for 3 years at simple in-
terest 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?
P× t× r
Answer: Interest for Fabina =
100
12500 × 3 × 12
= = 4500
100
10
Amount for Radha = 12500(1+ )³
100
11 11 11
= 12500 × × × = 16637.50
10 10 10
Interest for Radha = 16637.50-12500=4137.50
Interset paid by Fabina is Rs. 362.50 more than that paid by radha
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 compound interest,
what extra amount would I have to pay?
Answer: The extra amount payable would be interest on the first year’s interest
1st year’s interest = 12000 × 6%=720
Interest on 720 = 720 × 6%=43.20
Extra amount payable = Rs. 43.20
6. Arif took a loan of Rs 80,000 from a bank. If the rate of interest is 10%
per annum, find the difference in amounts he would be paying after 1.5
years if the interest is
(i) compounded annually.
Answer: rate of interest will become half and time will be three half years.
5
Amount = 80000(1+ )³
100
21 21 21
= 80000 × × × = 92610
20 20 20
5
Answer: Amount = 8000(1+ )²
100
21 21
= 8000 × × = 8820
20 20
Interest after 2 years = 8820-8000=820
8. Find the amount and the compound interest on Rs 10,000 for 1.5 years at
10% per annum, compounded half yearly. Would this interest be more than
the interest he would get if it was compounded annually?
5
Answer: Amount = 10000(1+ )³
100
21 21 21
= 10000 × × × = 11576.25
20 20 20
Interest = 11576.25-10000=1576.25
This interest would be more than the interest compounded annually, as interest com-
pounded half yearly is always more than compounded annually at the same rate of
interest.
9. Find the amount which Ram will get on Rs 4096, if he gave it for 18
months at 12.5% per annum, interest being compounded half yearly.
25
Answer: Amount = 4096(1+ )³
400
17 17 17
= 4096 × × × = 4913
16 16 16
21 21
Answer: Population in 2005 = 54000( × )=59535
20 20
11. In a Laboratory, the count of bacteria in a certain experiment was in-
creasing at the rate of 2.5% per hour. Find the bacteria at the end of 2
hours if the count was initially 5, 06,000.
5
Final Count after 2 hrs = 506000(1+ )²
200
41 41
= 506000 × × = 531616.25 which is 531616 in round figures
40 40
12. A scooter was bought at Rs 42,000. Its value depreciated at the rate of
8% per annum. Find its value after one year.