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Chapter 13 Direct and Indirect Proportions Ex 13.1 Solutions

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

Answer - 1 : -

We have the ratio of time period and the parking charge.

Hence the given quantities are not directly proportional.

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.

Answer - 2 : - Let the number to be filled in the blanks be a, b, c and d respectively.


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 required red pigment be x part.

Hence, the required amount of red pigment = 24 parts.

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 required number of bottles be x.

Hence the required number of bottles = 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 : - Let the actual length be x 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?

Answer - 6 : - Let the required length of the model ship be x m.


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?

Answer - 7 : - Let x be the number of sugar crystals needed.



Question - 8 : -
Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road of 72 km. What would be her distance covered in the map?

Answer - 8 : -

Let the required distance be x km.

Hence the distance covered in the map = 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 : - (i) Let the required length of shadow be x m.



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 the required distance be x km.

Hence the required distance = 168 km.

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