ADDITIONAL QUESTIONS AND ANSWERS:
1). Find the ratio of 5 km to 500 m
Ans: 1 km = 1000 m
5 km = 5000 m
5 km : 5000 m : 500 = 5000/500 = 10/1 = 10 : 1
2). State whether the following ratios are equivalent or not.
i) 1 : 2 and 2 : 3
ii) 2 : 3 and 4 : 5
iii) 1 : 3 and 2 : 6
Ans:
i) Given ratio = 1 : 2 and 2 : 3
1/( 2 ) and 2/( 3 )
LCM of 2, 3 = 6 ∴ 1/( 2 ) = (1 × 3)/(2 ×3 ) , ( 2 × 2 )/(3 ×2 ) = 4/( 6 )
We find that 3/( 6 ) < 4/( 6 ) which means 1/( 2 ) < 2/( 3 )
Hence the ratio 1 : 2 is not equivalent to 2 : 3
ii) Given ratio = 2 : 3 and 4 : 5
2/( 3 ) and 4/( 5 )
LCM of 3, 5 = 15 ∴ = (2 × 5)/(3 × 5 ) = 10/( 15 ), ( 4 × 3 )/(5 × 3 ) = 12/( 15 )
We find that 10/( 15 ) < 12/( 15 ),which means 2/( 3 ) < 4/( 5 )
Hence the ratio of 2 : 3 is not equivalent to 4 : 5
iii) Given ratio = 1 : 3 and 2 : 6
1/( 3 ) and 2/( 6 )
LCM of 3, 6 = 6 ∴ = (1 × 2)/(3 × 2 ) = 2/( 6 ), ( 2 × 1 )/(6 × 1 ) = 2/( 6 )
We find that 2/( 6 ) = 2/( 6 ),which means 1/( 3 ) < 2/( 6 )
Hence 1 : 3 is equivalent to 2: 6
3). Find:
i) 9 is 25% of what number
ii) 75% of what number is 15?
iii) A number whose 6% is 12.
Ans: i) Let the required number be x
So, 25% of x is 9
25/( 100 ) × x = 9
x = (9 × 100 )/25 = x ⇒ 900/25 = x ∴ x= 36
∴ The required number is 36.
ii) Let the required number be x
So, 75% of x is 15
75/( 100 ) × x = 15
x = (15 × 100 )/75 ⇒ x = 1500/75 ∴ x = 20
∴ The required number is 20.
iii) Let the required number be x
So, 6% of x is 12
6/( 100 ) × x = 12
x = (12 × 100 )/6 ⇒ x = 1200/6 ∴ x = 200
∴ The required number is 200.
4). Find the ratio of:
i) 2 hours to 160 minutes
ii) 8 mm to 24 cm
iii) 18 rupees to 90 paise
iv) 3 months to 2 years
Ans: i) 1 hour = 60 minutes
2 hours = 2 ×60 minutes = 120 minutes
Ratio of 2 hours to 160 minutes
= 120 : 160 = 3: 4
ii) 1 m = 10 cm
8 mm = 80 cm
Ratio of 8 mm to 24 cm is = 80 : 24 = 10 : 3
iii) 1 Rupee = 100 paise
18 rupees = 1800 paise
Ratio of 18 rupees to 90 paise = 1800 : 900 = 20 : 1
iv) 1 year = 12 months
2 years = 2 ×12 = 24 months
Ratio of 3 months to 2 years = 3 : 24 = 1 : 8
5). 12 bowls set cost ₹ 240. What would be the cost of 16 such bowls?
Ans: Cost of 12 bowls is ₹ 240
So, cost of 1 bowl = ₹ ( 240 )/( 12 )
Hence, cost of 16 bowls = ₹ ( 240 )/( 12 ) × 16 = ₹ 320.
6). Find the following:
i) Out of 32 students, 8 are absent. What percent of the students are absent?
Ans: Total Number of Students = 32
Number of students absent = 8
Percentage of students absent = 8/32 × 100% = 1/4 × 100% = 25%
ii) There are 25 radios, 16 of them are out of order. What percent of radios are out of order?
Ans: Total number of radios = 25
Radios out of order = 16
Percentage of radios out of order = 16/25 × 100% = 16 × 4% = 64%
iii) There are 120 voters, 90 of them voted yes. What percent voted yes and what percent voted number?
Ans: Total Number of voters = 120
Number of voted yes = 90
Percentage of voters voted yes = 90/( 120 ) × 100% = (300% )/( 4 ) = 75%
Number of voters voted no = 120 – 90 = 30
Percentage of voters voted no = 30/( 120 ) × 100% = (100% )/( 4 ) = 25%
iv) If 65% of students in a class have a bicycle, what percent of the student do not have bicycles?
Ans: Percentage of students having bicycle = 65%
Percentage of students not having bicycle = 100% – 65% = 35%
v) 8% of children of a class of 25 like getting wet in the rain. How many children like getting wet in the rain?
Ans: Total number of children in a class = 25
Percentage of children getting wet in the rain = 8%
∴ Number of children like getting wet in the rain = 8% of 25
= 8/(100 ) × 25 = 8/( 4 ) = 2
∴ 2 children like getting wet in the rain.
7. Find
a) 50% of 16 b) 75% of 12
Ans: a) = 50/100 × 164 b) = 75/( 100 ) × 12
= 164/2 = 82 = 3 ×3 = 9
8. Find percentage of increase or decrease:
i) Price of shirt decreased from ₹ 80 to ₹ 60.
Ans: Original amount = ₹ 80
Amount change = 80 – 60 = ₹ 20
Percentage of decrease = (amount change)/(original amount ) × 100
= 20/( 80 ) × 100 = 25%
ii) Marks in a test increased from 20 to 30.
Ans: Original marks = Initial marks = 20
Marks change = Final marks = 30 – 20 = 10
Percentage of increase = (marks change)/(original marks ) ×100
= 10/( 20 ) × 100 = 10 × 5 = 50% ∴ Percentage of increase in marks = 50%
3). Heena’s mother says, that in her childhood petrol was ₹ 1 a litre. It is ₹ 52 per litre today. By what percentage has the price gone up?
Ans: Original amount = ₹ 1
Amount change = 52 – 1
Percentage of increase = (amount change)/(original amount ) ×100
= 51/( 1 ) × 100 = 5100% ∴ Percentage of increase = 5100%
4). A Shopkeeper bought a chair of ₹ 375 and sold it for ₹ 40. Find the gain percentage.
Ans: Cost price of chair = ₹ 375
Selling price of chair = ₹ 400
Profit = SP – CP
= 400 – 375 = 25
Gain/ Profit % = profit/cp ×100
= 25/( 375 ) × 100 = ( 100)/( 15 ) = ( 20)/ 3 % ∴ Profit % = 20/ 3 %
5).( 20)/ 3 % has ₹ 2,400 in her account and the interest rate is 5%. After how many years would she earn ₹ 2,400 as interest?
Ans: P = ₹ 2,400 R = 5% I = ₹ 240 T = ?
I = (P × T × R)/100
T = (I × 100)/(P × R)
= (240 × 100)/(2400 × 5) = ( 10)/( 5 ) = 2 years ∴ Meena earns ₹ 2,400 as interest in 2 years.
6). On a certain sum the interest paid after 3 years is ₹ 450 at 5% rate of interest per annum. It earn ₹ 2,400 as interest?.Find the sum
Ans: I = ₹ 450 T = 3 years R = 5% P = ?
I = (P × T × R)/100
P = (I × 100)/(R × T)
= (450 × 100)/(5 × 3 ) = 30 ×100 = ₹ 3,000 ∴ The sum is ₹ 3,000