Anita has to drive from village A to village B. She measures a distance of 3.5 cm between these villages on the map. What is the actual distance between the villages if the map scale is 1 cm = 20 km?
Distance from village A to B on the map = 3.5 cm
Scale of map 1 cm = 20 km
Let actual distance = x km
So, 1: 3.5 = 20: x
1/3.5 = 20/x
x = (20 × 3.5)/1
x = 70 km
Distance between village A and village B is 70 km.
The mass of an aluminium rod varies directly with its length. If a 16 cm long rod has a mass of 192 g, find the length of the rod whose mass is 105 g.
Length of rod = 16 cm and mass = 192 g
If mass is 105 g, then
Let length of rod = x cm
So, 16: x = 192: 105
16/x = 192/105
x = (16 × 105)/192
= 35/4
= 8.75 cm
Length of rod = 8.75cm.
In a model of a ship, the mast (flagstaff) is 6 cm high, while the mast of the actual ship is 9 m high. If the length of the ship is 33 m, how long is the model of the ship?
Height of a model of ship = 6 cm
But height of actual ship = 9 m
If length of ship = 33 m
Let length of model be ‘x’
So, 6: x = 9 m: 33
6/x = 9/33
x = (6 × 33)/9
Length of model is 22 cm.
If the thickness of a pile of 12 cardboard sheets is 45 mm, then how many sheets of the same cardboard would be 90 cm thick?
It is given that,
Thickness of 12 cardboard = 45 mm
Let ‘x’ be the number of cardboard whose thickness is 90 cm = 900 m
So, 12: x = 45: 900
12/x = 45/900
x = (12 × 900)/45
= 240 mm
Thickness of 90 cardboard is 240 mm.
If a car travels 67.5 km in 4.5 liters of petrol, how many kilometers will it travel in 26.4 liters of petrol?
Let car travels ‘x’ km in 26.4 liters of petrol.
So,
Distance (in km) | x | 67.5 |
Petrol (in L) | 26.4 | 4.5 |
We know that it is a direct variation.
So, x: 26.4 = 67.5: 4.5
x/26.4 = 67.5/4.5
x = (67.5 × 26.4)/4.5
= 396 km
If 175 dollars cost 7350, how many dollars can be purchased in 24024?
Let ‘x’ dollars be purchased in 24024
So,
Cost (in ) | 7350 | 24024 |
Dollars | 175 | x |
We know that it is a direct variation.
So, 7350: 175 = 24024: x
7350/175 = 24024/x
x = (24024 × 175)/7350
= 572 Dollars
If a labourer earns 672 per week, how much will he earn in 18 days?
Let the labourer earn x in 18 days
So,
Days | 7 | 18 |
Money earned (in ) | 672 | x |
We know that it is a direct variation.
So, 7: 672 = 18: x
7/672 = 18/x
x = (18 × 672)/7
= 1728
If 8 meters cloth costs 250, find the cost of 5.8 meters of the same cloth.
Let the cost of 5.8 m cloth be x
So,
Length (in m) | 8 | 5.8 |
Cost of cloth (in) | 250 | x |
We know that it is a direct variation.
So, 8: 250 = 5.8: x
8/250 = 5.8/x
x = (5.8 × 250)/8
= 181.25
. If x and y are in direct variation, complete the following tables:
(i)
x | 3 | 5 | … | … | 10 |
y | 45 | … | 90 | 120 | … |
(ii)
x | 4 | 8 | … | 20 | 28 |
y | 7 | … | 21 |
(i) It is given that,
x/y = 3/45 = 1/15
x/y is constant with 1/15.
Hence, x and y are directly proportional.
Now,
x1/y1 = 1/15 => 5/y1 = 1/15
y1 = 5 × 15 = 75
x2/y2 = x2/90 = 1/15
x2 = 90/15 = 6
x3/y3 = x3/120 = 1/15
x3 = 120/15 = 8
x4/y4 = 10/y4 = 1/15
y4 = 10 × 15 = 150
Here is the complete table:
x | 3 | 5 | 6 | 8 | 10 |
y | 45 | 75 | 90 | 120 | 150 |
(ii) It is given that,
x/y = 4/7
x/y is constant with 4/7.
Hence, x and y are directly proportional.
Now,
x1/y1 = 8/y1 = 4/7
y1 = (8 × 7)/4 = 14
x2/y2 = x2/21 = 4/7
x2 = (21 × 4)/7 = 12
x3/y3 = 21/y3 = 4/7
y3 = (21 × 7)/4 = 35
x4/y4 = 28/y4 = 4/7
y4 = (28 × 7)/4 = 49
Here is the complete table:
x | 4 | 8 | 12 | 20 | 28 |
y | 7 | 14 | 21 | 35 | 49 |
Observe the following tables and find if x and y are directly proportional:
(i)
x | 5 | 8 | 12 | 15 | 18 | 20 |
y | 15 | 24 | 36 | 60 | 72 | 100 |
(ii)
x | 3 | 5 | 7 | 9 | 10 |
y | 9 | 15 | 21 | 27 | 30 |
(i) It is given that,
x/y = 5/15 = 1/3
Similarly,
x/y = 8/24 = 1/3
x/y = 12/36 = 1/3
But, x/y = 15/60 = 1/4
x/y = 18/72 = 1/4
x/y = 20/100 = 1/5 which is not equal to 1/3
so, x/y is not constant.
Hence, x and y are not directly proportional.
(ii) It is given that,
x/y = 3/9 = 1/3
Similarly,
x/y = 5/15 = 1/3
x/y = 7/21 = 1/3
x/y = 9/27 = 1/3
x/y = 10/30 = 1/3
so, x/y is constant.
Hence, x and y are directly proportional.
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