Long Answer TypeA 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 and (ii) the height of a pole which casts a shadow 5 m long.
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?
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.
Solution: We draw the following squares I, II, III, IV and V having the length of side as 1 cm, 2 cm, 3 cm, 4 cm and 5 cm respectively.
Now, we have
Obviously:
(a) The length of a side (L) and the perimeter of the square (P) are in the direct proportion.
(b) But the length of a square (L) and the area of the square (A) are not in the direct proportion.
Question: 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 Type1. Which 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.
Long Answer TypeIn 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°?
Short Answer TypeIf a box of sweets is divided among 24 children, they will get 5 sweets each. How many would each get, if the number of the children is reduced by 4?
A farmer has enough food to feed 20 animals in his cattle for 6 days. How long would the food last if there were 10 more animals in his cattle?
A contractor estimates that J persons could rewire jasminder’s house in 4 days. If, he uses 4 persons instead of three, how long should they take to complete the job?
Switch
