### NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1

**Ex 13.1 Class 8 Maths 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.**

**Solution:**

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

Hence the given quantities are not directly proportional.

**Ex 13.1 Class 8 Maths 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:**

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

**Ex 13.1 Class 8 Maths 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 the required red pigment be x part.

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

**Ex 13.1 Class 8 Maths 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 required number of bottles be x

Hence the required number of bottles = 700.

**Ex 13.1 Class 8 Maths 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?**

**Solution:**

Let the actual length be x cm.

**Ex 13.1 Class 8 Maths 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 the required length of the model ship be x m.

**Ex 13.1 Class 8 Maths Question 7.**

**Suppose 2 kg of sugar contains 9 × 10 ^{6} crystals. How many sugar crystals are there in**

**(i) 5 kg of sugar?**

**(ii) 1.2 kg of sugar?**

**Solution:**

Let x be the number of sugar crystals needed.

**Ex 13.1 Class 8 Maths 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?**

**Solution:**

Let the required distance be x km.

Hence the distance covered in the map = 4 cm.

**Ex 13.1 Class 8 Maths 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:**

(i) Let the required length of shadow be x m.

**Ex 13.1 Class 8 Maths 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 required distance be x km.

Hence the required distance = 168 km.