Exercise 13.1
Question 1:
Following are the car parking charges near a railway station up to:
Check if the parking charges are in direct proportion to the parking time.
Answer 1:
Here, the charges per hour are not same, i.e., C1 ≠ C2 ≠ C3 ≠C4
Therefore, the parking charges are not in direct proportion to the parking time.
Question 2:
A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base. In the following table, find the parts of base that need to be added.
Parts of red pigment | 1 | 4 | 7 | 12 | 20 |
Parts of base | 8 | — | — | — | — |
Answer 2:
Parts of red pigment | 1 | 4 | 7 | 12 | 20 |
Parts of base | 8 | 32 | 56 | 96 | 160 |
Question 3:
In Question 2 above, if 1 part of a red pigment requires 75 mL of base, how much red pigment should we mix with 1800 mL of base?
Answer 3:
Let the parts of red pigment mix with 1800 mL base be x
Parts of red pigment | 1 | X |
Parts of base | 75 | 1800 |
Hence, with base 1800 mL, 24 parts red pigment should be mixed.
Question 4:
A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?
Answer 4:
Let the number of bottles filled in five hours be x.
Hours | 1 | X |
Bottles | 75 | 1800 |
Hence, the number of bottles filled in five hours be 700.
Question 5:
A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm as shown In the diagram. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?
Answer 5:
Length | 5 | X |
Enlarged length | 50,000 | 20,000 |
Here length and enlarged length of bacteria are in direct proportion
Question 6:
In a model of a ship, the mast is 9 cm high, while the mast of the actual ship is 12 m high. If the length if the ship is 28 m, how long is the model ship?
Answer 6:
Let the length of model ship be x
Length of actual ship (in m) | 12 | 28 |
Length of model ship (in cm) | 9 | X |
Here length of mast and actual length of ship are in direct proportion
Hence, the length of the model ship is 21 cm.
Question 7:
Suppose 2 kg of sugar contains 9 x 106 crystals. How many sugar crystals are there in
(i) 5 kg of sugar?
(ii) 1.2 kg of sugar?
Answer 7:
Let sugar crystals be x.
Weight of sugar (in kg) | 2 | 5 |
No. of crystals | 9x106 | X |
Hence, the number of sugar crystals is 2.25 x 107.
(ii)
Let sugar crystals be x.
Weight of sugar (in kg) | 2 | 1.2 |
No. of crystals | 9x106 | X |
Hence, the number of sugar crystals is 5.4 x 106.
Question 8:
Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for 72 km. What would be her distance covered in the map?
Answer 8:
Let distance covered in the map be x.
Actual distance (in km) | 18 | 72 |
Distance covered in map (in cm) | 1 | X |
Here actual distance and distance covered in the map are in direct proportion.
Hence, distance covered in the map is 4 cm
Question 9:
A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time
(i) the length of the shadow cast by another pole 10 m 50 cm high
(ii) the height of a pole which casts a shadow 5 m long.
Answer 9:
Here height of the pole and length of the shadow are in direct proportion.
And 1 m = 100 cm
5 m 60 cm = 5 x 100 + 60 = 560 cm
3 m 20 cm = 3 x 100 + 20 = 320 cm
10 m 50 cm = 10 x 100 + 50 = 1050 cm
5 m = 5 x 100 - 500 cm
(i) Let the length of the shadow of another pole be x.
Height of pole (in cm) | 560 | 1050 |
Length of shadow (in cm) | 320 | X |
Hence, the length of the shadow of another pole be 6m.
Let the hight of the pole be x.
Height of pole (in cm) | 560 | x |
Length of shadow (in cm) | 320 | 500 |
Hence, the hight of the pole be 8m 75 cm
Question 10:
A loaded truck travels 14 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours?
Answer 10:
Let distance covered in 5 hours be .r km.
1 hour = 60 minutes
5 hours = 5 x 60 = 300 minutes
Distance (in km] | 14 | X |
Time (in minutes) | 25 | 300 |
Here distance covered and time in direct proportion.
1. What are direct and inverse proportions? |
2. How can we identify if two variables are in direct or inverse proportion? |
3. What are some real-life examples of direct and inverse proportion? |
4. What is the difference between direct and inverse proportion? |
5. How can we solve problems related to direct and inverse proportions? |
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