NCERT Solutions for Class 8 Maths Exercise 13.1

NCERT Solutions for Class 8 Maths Exercise 13.1 Class 8 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 8 Maths chapter wise NCERT solution for Maths Book all the chapters can be downloaded from our website and myCBSEguide mobile app for free

NCERT solutions for Class 8 Maths Direct and Inverse Proportions Download as PDF

NCERT Solutions for Class 8 Maths Direct and Inverse Proportions

Class –VIII Mathematics(Ex. 13.1)

NCERT SOLUTION

1.Following are he car parking charges near a railway station up to:

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.

Ans.  Charges per hour:

 = Rs.15

 = Rs.12.50

 = Rs.11.67

 = Rs.7.50

Here, the charges per hour are not same, i.e.,

Therefore, the parking charges are not in direct proportion to the parking time.

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2. 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.

Ans. Let the ratio of parts of red pigment and parts of base be

Here

 =  (say)

When

   

When

   

When

   

When

   

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NCERT Solutions for Class 8 Maths Exercise 13.1

3. 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?

Ans. Let the parts of red pigment mix with 1800 mL base be

Since it is in direct proportion.

 

parts

Hence with base 1800 mL, 24 parts red pigment should be mixed.

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NCERT Solutions for Class 8 Maths Exercise 13.1

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

Ans. Let the number of bottles filled in five hours be

Here ratio of hours and bottles are in direct proportion.

 

bottles

Hence machine will fill 700 bottles in five hours.

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NCERT Solutions for Class 8 Maths Exercise 13.1

5. 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?

Ans. Let enlarged length of bacteria be .

Actual length of bacteria

=  cm =  cm

Here length and enlarged length of bacteria are in direct proportion.

 

= 2 cm

Hence the enlarged length of bacteria

is 2 cm.

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NCERT Solutions for Class 8 Maths Exercise 13.1

6. 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 if the ship is 28 m, how long is the model ship?

Ans. Let the length of model ship be

Here length of mast and actual length of ship are in direct proportion.

 

= 21 cm

Hence length of the model ship is 21 cm.

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NCERT Solutions for Class 8 Maths Exercise 13.1

7. Suppose 2 kg of sugar contains 9  crystals. How many sugar crystals are there in (i) 5 kg of sugar? (ii) 1.2 kg of sugar?

Ans. (i) Let sugar crystals be

Here weight of sugar and number of crystals are in direct proportion.

=

Hence the number of sugar crystals is

(ii)  Let sugar crystals be

Here weight of sugar and number of crystals are in direct proportion.

 

=

Hence the number of sugar crystals is

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NCERT Solutions for Class 8 Maths Exercise 13.1

8. 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?

Ans. Let distance covered in the map be

Here actual distance and distance covered in the map are in direct proportion.

 

 

  = 4 cm

Hence distance covered in the map is 4 cm.

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NCERT Solutions for Class 8 Maths Exercise 13.1

9. 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 5 m long.

Ans. Here height of the pole and length of the shadow are in direct proportion.

And 1 m = 100 cm

5 m 60 cm = 5  100 + 60 = 560 cm

3 m 20 cm = 3  100 + 20 = 320 cm

10 m 50 cm = 10  100 + 50 = 1050 cm

5 m = 5  100 = 500 cm

(i) Let the length of the shadow of another pole be

 = 600 cm = 6 m

Hence length of the shadow of another pole is 6 m.

(ii) Let the height of the pole be

 

= 875 cm = 8 m 75 cm

Hence height of the pole is 8 m 75 cm.

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NCERT Solutions for Class 8 Maths Exercise 13.1

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

Ans. Let distance covered in 5 hours be km.

1 hour = 60 minutes

5 hours = 5  60 = 300 minutes

Here distance covered and time in direct proportion.

 

 = 168 km

NCERT Solutions for Class 8 Maths Exercise 13.1

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