(a) 15, 16, 20, 21 (b) 18, 24, 9, 12 (c) 25, 75, 12, 36
6. Which of the following statements are true?
(a) 20 kg : 80 kg = 100: 300 (b) 80 m : 20 m = 14 m : 3.5 m
Answers
Write True (T) or False (F) against each of the following statements:
(a) 16:24::20:30
(b) 21:6::35:10
(c) 12:18::28:12
(d) 8:9::24:27
(e) 5.2:3.9::3:4
(f) 0.9:0.36::10:4
Answer
If the ratio of first to the second is equal to ratio to third to the fourth, these will be in proportion
S.no
Problem
First to second ratio
third to fourth ratio
Answer(T/F)
a)
16:24::20:30
16
24
=
2
:
3
20
30
=
2
:
3
True
b)
21:6::35:10
21
6
=
7
:
2
35
10
=
7
:
2
True
c)
12:18::28:12
12
18
=
2
:
3
28
12
=
7
:
3
False
d)
8:9::24:27
8:9
24
27
=
8
:
9
False
e)
5.2:3.9::3:4
5.2
3.9
=
4
:
3
3:4
False
f)
0.9:0.36::10:4
.9
.36
=
90
36
=
10
4
10:4
True
Question 3
Are the following statements true?
(a) 40 persons: 200 persons = Rs 15: Rs 75
(b) 7.5 litres: 15 litres = 5 kg: 10 kg
(c) 99 kg: 45 kg = Rs 44: Rs 20
(d) 32 m: 64 m = 6 secs: 12 sec
(e) 45 km: 60 km = 12 hours: 15 hours
Answer
S.no
Problem
Left hand side ratio
Right hand side ratio
Answer(T/F)
a)
40 persons: 200 persons = Rs 15: Rs 75
40
200
=
1
:
5
15
75
=
1
:
5
True
b)
7.5 litres: 15 litres = 5 kg: 10 kg
7.5
15
=
1
:
2
5
10
=
1
:
2
True
c)
99 kg: 45 kg = Rs 44: Rs 20
99
45
=
11
:
5
44
20
=
11
:
5
True
d)
32 m: 64 m = 6 secs: 12 secs
32
64
=
1
:
2
6
12
=
1
:
2
True
e)
45 km: 60 km = 12 hours: 15 hours
45
60
=
3
:
4
12
15
=
4
:
5
False
Question 4
Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
(a) 25 cm: 1 m and Rs 40: Rs 160
(b) 39 litres: 65 litres and 6 bottles: 10 bottles
(c) 2 kg: 80 kg and 25 g: 625 g
(d) 200 mL: 2.5 litre and Rs 4: Rs 50
Answer
When the units are different in one ratio, we need to convert the bigger unit into smaller unit
S.no
LHS ratio
RHS ratio
Middle terms
Extreme terms
a)
1 m= 100 cm
So 25 cm:100 cm
= 1:4
40/160
1:4
100cm and Rs 40
25 cm and Rs 160
b)
39/65=3:5
6/10= 3/5
65 litres and 6 bottles
39 litres and 10 bottles
c)
2/80= 1/40
25/625= 1/25
NA as they are not proportional
NA
d)
2.5 litre= 2500 ml
So 200/2500
=4/50= 2/25
4/50= 2/25
2500 ml and Rs 4
200ml and Rs 50
Exercise 12.3
Question 1
If the cost of 7 m of cloth is Rs 294, find the cost of 5 m of cloth.
Answer
In these type of question, we need to find the value per unit value which is find by dividing the quantity given
Cost of 7 m of cloth = Rs 294
So, the cost of 1 m of cloth =
294
7
= Rs 42
Cost of 5 m of cloth =
42
×
5
= Rs 210
Question 2
Ekta earns Rs 1500 in 10 days. How much will she earn in 30 days?
Answer
Amount Ekta earns in 10 days = Rs 1500
So, amount earned in 1 day by Ekta = Rs 1500 ÷ 10 = Rs.
Money she will earn in 30 days = Rs. 150 × 30 = Rs. 4500
Question 3
If it has rained 276 mm in the last 3 days, how many cm of rain will fall in one full week (7 days)? Assume that the rain continues to fall at the same rate.
Answer
Amount of rain in 3 days = 276 mm = 27.6 cm
So, Amount of rain in 1 day = 27.6 ÷ 3 = 9.2 cm
We know that one week has 7 days.
So, Amount of rain in 7 days =
9.2
×
7
=
64.4
c
m
Question 4
Cost of 5 kg of wheat is Rs 30.50.
(a) What will be the cost of 8 kg of wheat?
(b) What quantity of wheat can be purchased in Rs 61?
Answer
Given
Cost of 5 kg of wheat = Rs. 30.50
So, Cost of 1 kg = Rs. 30.50 ÷ 5 = Rs. 6.10
a) Cost of 8 kg of wheat = 8 × (cost of 1 kg of wheat)=8 × Rs. 6.10 = Rs. 48.80
b) Amount of wheat purchased for Rs. 6.10 = 1 kg
Amount of wheat purchased for Rs 61 = 61 ÷ 6.10 =
6100
610
=
10
k
g
Question 5
The temperature dropped 15 degrees Celsius in the last 30 days. If the rate of temperature drop remains the same, how many degrees will the temperature drop in the next ten days?
Answer
Temperature drop in 30 days = 15°C
Rate of Temperature drop in 1 day = 15 ÷ 30 = (½)°C
Temperature drop in 10 days = (½)°C × 10 = 5°C
Question 6
Shaina pays Rs 7500 as rent for 3 months. How much does she has to pay for a whole year, if the rent per month remains same?
Answer
Rent paid by Shaina for 3 months = Rs 7500
Rent paid by Shaina per month = 7500 ÷ 3 = Rs 2500
We know that in a year, there are 12 months.
So, the rent paid by Shaina for whole year =
2500
×
12
= Rs 30,000
Question 7
Cost of 4 dozen bananas is Rs 60. How many bananas can be purchased for Rs 12.50?
Answer
We know that
1 dozen = 12
So, 4 dozen contain 48 bananas
Now The cost of 48 bananas is given as Rs. 60
So Cost of 1 banana= 60 ÷ 48 = 5 ÷ 4 = Rs 1.25
Number of bananas purchased in Rs 12.50 =
T
o
t
a
l
R
u
p
e
e
s
P
r
i
c
e
o
f
o
n
e
b
a
n
a
n
a
=
12.5
1.25
=
10
Question 8
The weight of 72 books is 9 kg. What is the weight of 40 such books?
Answer
Given
Weight of 72 books = 9 kg
So, Weight of 1 book = 72 ÷ 9 = 8 Kg
Now Weight of 40 books =
40
×
8
=
320
k
g
Question 9
A truck requires 108 litres of diesel for covering a distance of 594 km. How much diesel will be required by the truck to cover a distance of 1650 km?
Answer
Amount of Diesel required by truck for covering a distance for 594 km = 108 l
Amount of Diesel required by truck for covering a distance for 1 km = 108 ÷ 594 = (2/11) litre
So, Amount of diesel required by truck for covering a distance for 1650 km 9
.
Answer:
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