MP Board Class 8th Maths Solutions Chapter 13 Direct and Inverse Proportion Ex 13.1

MP Board Class 8th Maths Solutions Chapter 13 Direct and Inverse Proportion Ex 13.1

Question 1.
Following are the car parking charges near a railway station upto
4 hours ₹ 60
8 hours ₹ 100
12 hours ₹ 140
24 hours ₹ 180
Check if the parking charges are in direct proportion to the parking time.
Solution:

∴ The parking timing is not in direct proportion with parking charges.

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.

Solution:

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?
Solution:
Let x part of red pigment is mixed with 1800 mL of base.

Question 4.
A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?
Solution:
Let the number of bottles which will be filled in five hours be x

Question 5.
A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm as shown in diagram. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?

Solution:
Let the enlarged length of bacteria be x cm.
∵ 50,000 times enlarged bacteria attains a length of 5 cm.

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 of the ship is 28 m, how long is the model ship?
Solution:
Let x m be the length of the model ship when the height of the mast is 9 cm.
Now, according to question,

Thus, length of the model ship = 0.21 m
= 21 cm

Question 7.
Suppose 2 kg of sugar contains 9 × 10⁶ crystals. How many sugar crystals are there in
(i) 5 kg of sugar ?
(ii) 1.2 kg of sugar ?
Solution:
Let the crystals contained by 5 kg and 1.2 kg of sugar be x and y respectively.

Thus, 5 kg and 1.2 kg of sugar contains 2.25 × 10⁷ and 5.4 × 10⁶ crystals respectively.

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?
Solution:
Let the distance covered in the map be x cm.

Thus, the distance covered by her 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.
Solution:
Let x be the length of shadow cast by the pole of a height 10 m 50 cm and y be the height of the vertical pole which cast a shadow 5 m long.

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?
Solution:
Let the distance travelled by truck in 5 hours be x km

∴ Distance travelled by the truck in 5 hours is 168 km.

MP Board Class 8th Maths Solutions