# NCERT Class 8 Mathematics Solutions: Chapter 13 – Direct and Inverse Proportions Exercise 13.1 Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

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1. Rashmi has a road map with a scale of representing . She drives on a road for . What would be her distance covered in the map?

Consider distance covered in the map be .

 Actual distance (in km) Distance covered in map (in cm)

Actual distance and distance covered in the map are in direct proportion.

So, the distance covered in the map is .

2. A high vertical pole casts a shadow long. Find at the same time

(i) The length of the shadow cast by another pole high

(ii) The height of a pole which casts a shadow long.

Height of the pole and length of the shadow are in direct proportion.

And

(i) Consider,

The length of the shadow of another pole be .

 Height of pole (in cm) Length of shadow (in cm)

So, the length of the shadow of another pole is .

(ii) Consider,

The height of the people be .

 Height of pole (in cm) Length of shadow (in cm)

So, the length of the shadow of another pole is .

3. A loaded truck travels 14 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours?

Consider,

Distance covered in 5 hours be x km

∵ 1 hour = 60 minutes

∵ 5 hours = 5 × 60

= 300 minutes

Distance (in km) 14 x

Time (in minutes) 25 300

Distance covered and time in direct proportion.

⇾ 14/25 = x/300

⇾ x × 25 = 14 × 300

⇾ x = (14 × 300) /25

⇾ 168 km

So, the distance covered in 5 hours is 168 km.

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