Exercise 13.1

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Q1. Following are the car parking charges near a railway station upto

4 hours Rs 60

8 hours Rs 100

12 hours Rs 140

24 hours Rs 180

Check if the parking charges are in direct proportion to the parking time.

Solution :

Q2. 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.

Q3. 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:

Q4. A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?

Solution:

Q5. 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?

Q6. 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?

Therefore the length of model ship is 21 cm. 

Q7. Suppose 2 kg of sugar contains 9 × 10⁶ crystals.

How many sugar crystals are there in

(i) 5 kg of sugar?

(ii) 1.2 kg of sugar?

Solution:

Q8. Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for 72 km. What would be her distance covered in the map?

Q9.  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 5m long.

Solution:

Q10. A loaded truck travels 14 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours?

Solution:

Exercise 13.2                        

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Q1.  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.

Solution:

(i)  Numbers of workers on a job and time always be in inverse proportion because when we increase in workers time reduces and when we reduce in workers time it take more time.

(ii) The time taken and distance are in direct proportion because if we increase in time it covers more distance. Hence both quantities increase together.

(iii) As area will be cultivated as more crops will be harvested. So these are direct proportion.

(iv) Time and speed always be in inverse proportion. As we increase the time we have to reduce the speed to cover a fixed distance. Similarly we see that if we increase the speed time reduces automatically.

(v) If population is increased area land will be short to live. Therefore these both quantity are in inverse proportion.   

Q2.  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?

Solution: Prize will be distributed to winner in inverse proportion.

As both quantities are in inverse proportion.

Suppose the table has …

Q3.  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.

Solution:

The relation between spokes and angle between consecutive spokes are in inverse proportion.

Therefore,    X₁Y₁ = X₂Y₂

Q4.  If 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?

Solution:

According to question we have the table like this

raराम एक अच्चा लड़का है |

वह इसी गाँव में रहता है | 

मैं एक डॉक्टर हूँ |