NCERT Class 8 Mathematics Solutions: Chapter 13 – Direct and Inverse Proportions Exercise 13.1 Part 3

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Direct and inverse proportion are given in image

Understanding of Direct and Inverse Proportion

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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?

Answer:

Consider distance covered in the map be .

In given table actual distance and distance covered in map

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.

Answer:

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 .

In given table height of pole and length of shadow

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 .

In table height of pole and length of shadow

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?

Answer:

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.