Short Answer TypeA loaded truck travels 14 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours?
An electric pole, 14 metres high casts a shadow of 10 metres. Find the height of a tree that casts a shadow of 15 metres under similar conditions.
If the 750 sheets of thick paper is 21/2 kilograms, then how many sheets of the same paper would weigh 40 grams.
A train is moving at a uniform speed of 75 km/hour. (i) Find the time required to cover a distance of 250 km and (ii) How far will it travel in 20 minutes?
The scale of a map as 1: 30000000. Two cities are 4 cm apart on the map. Find the actual distance between them.
Long Answer TypeOn a squared paper, draw five squares of different sides. Write the following information in a tabular form.
|
Square 1 |
Square 2 |
Square 3 |
Square 4 |
Square 5 |
|
|
Length of a side (L) |
|||||
|
Perimeter (P) |
|||||
|
L/P |
|||||
|
L/A |
Find whether the length of a side is in direct proportion to:
(a) The perimeter of the square.
(b) The area of the square.
Observe the following tables and find which pair of variables (here x and y) are in inverse proportion.
(i)
|
X |
50 |
40 |
30 |
20 |
|
y |
5 |
6 |
7 |
8 |
(ii)
|
X |
100 |
200 |
300 |
400 |
|
y |
60 |
30 |
20 |
15 |
(iii)
|
X |
90 |
60 |
45 |
30 |
20 |
5 |
|
y |
10 |
15 |
20 |
25 |
30 |
35 |
Short Answer TypeWhich of the following are in inverse proportion?
(i) The number of workers on a job and the time to complete the job.
(ii) The time taken for a journey and the distance travelled in a uniform speed.
(iii) Area of cultivated land and the crop harvested.
(iv) The time taken for a fixed journey and the speed of the vehicle.
(v) The population of a country and the area of land per person.
If an increase in one quantity brings about a corresponding decrease in the other and vice versa, then the two quantities vary inversely.
(i) If number of workers are increased then time to complete the job would decrease.
∴ It is a case of inverse variation.
(ii) For longer distance, more time would be required.
∴ It is not a case of inverse variation
(iii) For more area of land, more crops would be harvested.
∴ It is not a case of inverse variation,
(iv) If speed is more, time to cover a fixed distance would be less.
∴ It is a case of inverse variation,
(v) For more population, less area per person would be required.
∴ It is a case of inverse variation.
In a television game show, the prize money of Rs 1,00,000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners?
|
Number of winners |
1 |
2 |
4 |
5 |
8 |
10 |
20 |
|
Prize for each winner (in Rs) |
1,00,000 |
50,000 |
... |
... |
... |
... |
... |
Rehman is making a wheel using spokes. He wants to fix equal spokes in such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table.
|
Number of spokes |
4 |
6 |
8 |
10 |
12 |
|
Angle between a pair of consecutive spokes |
90° |
60° |
... |
... |
... |
(i) Are the number of spokes and the angles formed between the pairs of consecutive spokes in inverse proportion?
(ii) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes.
(iii) How many spokes would be needed, if the angle between a pair of consecutive spokes is 40°?
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