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**Number Line Prime Class 6 Solutions Chapter 8 Ratio Proportion and Unitary Method**

Welcome to NCTB Solutions. Here with this post we are going to help 6th class students for the Solutions of Number Line Prime Class 6 Math Book, Chapter 8, Ratio, Proportion and Unitary Method. Here students can easily find step by step solutions of all the problems for Ratio, Proportion and Unitary Method, Exercise 8A, 87B, 8C, 8D, 8E, 8F and 8G Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 8 solutions. Here in this post all the solutions are based on latest Syllabus.

**Ratio, Proportion and Unitary Method Exercise 8A Solution :**

**Question no – (1) **

**Solution :**

**(a) 14/49**

= 2/7

**(b) 6/32**

= 3/16

**(c) 15/36**

= 5/12

**(d) 104/168**

= 13/21

**Question no – (2) **

**Solution :**

**(a) 18 : 108**

= 1 : 6

**(b) 40 × 60**

= 2400

**(c) 2400 : 28**

= 600 : 7

**Question no – (3) **

**Solution :**

**(a)** 2 : 3 -> 4 : 6

**(b)** 1 : 9 -> 2 : 18

**(c)** 5 : 4 -> 10 : 8

**(d)** 7 : 6 -> 14 : 12

**Question no – (4) **

**Solution :**

**(a)** Yellow fish to white fish

= 6 : 4

= 3 : 2

**(b)** Black fish to total fish

= 2 : (3 + 6 + 4 + 2)

= 2 : 15

**(c)** Red fish to black fish

= 3 : 2

**Question no – (5)**

**Solution :**

Math book : science book

= 4 : 5

So, fraction of science book

= 75

So, No of math book

= 4/5 × 75

= 60

**Question no – (6) **

**Solution :**

**(a)** 11 : 15 > 13 : 18

**(b)** 13 : 21 > 17 : 29

**(c)** 11 : 13 < 17 : 19

**Question no – (7)**

**Solution :**

Reema get,

= 11/21 × 777

= 407

Ritika,

= 10/21 × 777

= 370

So, difference between them (407 – 370)

= 37

**Question no – (8)**

**Solution :**

Car speed = 162/3

= 54 km/h

Scooter speed = 120/4

= 30 km/h

So, Ration = 54 : 30

= 9 : 5

**Ratio, Proportion and Unitary Method Exercise 8B Solution :**

**Question no – (1) **

**Solution :**

**(a)** 21 : 35 and 24 : 40

= 3 : 5 and 3 : 5 (Yes)

**(b)** 5 : 7 and 40 : 64

= 5 : 7 and 10 : 16 (No)

**(c)** 90 : 270 and 17 : 51

= 1 : 3 and 1 : 3

**(d)** 75 : 21 and 18 : 6

= 25 : 7 and 3 : 1

**Question no – (2) **

**Solution :**

**(a)** 4 : 5 : : 4 : 5

**(b)** 1 : 2 : : 3 : (2 × 3) = 6

**Question no – (3) **

**Solution :**

**(a) 500 : 450 : : 110 : 99**

=> 500 × 110

= 49500

= 450 × 99 (Yes)

**(b) 6 × 72**

= 432

= 24 × 18 (Yes)

**(c) 2 cm : 34 mm : : 1200g : 2kg 40g**

=> 20 mm : 34 mm : : 1200g : 2040g

20 × 2040

= 4080

= 34 × 1200 (Yes)

**(d) 250ml : 2000ml : : 48 minutes : 120 minutes**

=> 250 × 120

= 30000

≠ 2000 × 48 (No)

**Ratio, Proportion and Unitary Method Exercise 8C Solution :**

**Question no – (1)**

**Solution :**

Price of 10 balls is 50

Price of 1 balls is

= 50/10

Price of 15 balls

= 50/10 × 15

= Rs 75

**Question no – (2)**

**Solution :**

Price of 20 kg wheat is 600

Price of 1 kg wheat is 600/20

Price of 13 kg wheat

= 600/20 × 13

= Rs390

**Question no – (3)**

**Solution :**

In 4 acres trees are 50

In 1 acres tree are

= 50/4

In 10 acres trees are

= 50/4 × 10

= 125

**Question no – (4)**

**Solution :**

In 3 boxes no of pencils = 15

In 1 box no of pencils = 15/3

In 10 boxes no of pencils

= 15/3 × 10

= 50

**Question no – (5)**

**Solution :**

Cost of 184 km is 230

Cost of 1 km is = 230/184

Cost of 540 km is

= 230/184 × 540

= Rs 675

**Question no – (6)**

**Solution :**

In 5 hours, flies 4000 km

In 1 hour, flies 4000/5 km

So, in 8 hours the aeroplane flies

= 4000/5 × 8

= 6400 km

**Question no – (7)**

**Solution :**

75 envelopes cost Rs 600

1 envelope cost = 600/75

40 envelopes cost = 600/75 × 40 = Rs 320

**Question no – (8)**

**Solution :**

12 soap bars weight 960 kg

12 soap bars weight = 960/12

9 soap bars weight

= 960/12 × 19

= 720g

**Question no – (9)**

**Solution :**

In 9 kg flour of biscuits can be made 378

In 1 kg flour of biscuits can be made = 378/9

In 9 kg flour of biscuits can be made

= 378/9 × 19

= 798

**Question no – (10)**

**Solution :**

Fees for 5 days is Rs 1250

Fees for 1 day is 1250/5

Fees for 25 days is 1250/5 × 20

= Rs 6250

**Ratio, Proportion and Unitary Method Exercise 8D Solution :**

**Question no – (1) **

**Solution :**

**(a)** Speed

= 336/8

= 42 Km/h

**(b)** Speed

= 64/5

= 12.8 Km/ h

**(c)** Speed

= 650/13

= 50 Km/h

**(d)** Speed

= 195/3

= 65 Km/h

**Question no – (2)**

**Solution :**

Speed of the truck

= 576/8

= 72 Km/h

**Question no – (3)**

**Solution :**

3/1/2 hours

= 7/2 hours

So, Speed of the aero plane

= 2100/7/2

= 2100/7 x 2

= 600Km/h

**Question no – (4)**

**Solution :**

1 hours 20 minutes

= 80 minutes

= 80/60 hour

So, speed

= 96/80/60

= 96/80 x 60

= 720 Km/h

**Question no – (5)**

**Solution :**

4 hours 45 minutes.

= 240 min + 45 min

= 285 min

= 285/60 hour

So, speed of the train

= 252/285/60

= 252/285 x 60

= 1008 ÷ 19

= 53.05

= 53.05 Km/h

**Question no – (6)**

**Solution :**

Speed of Ram

= 32/40

= 0.8 Km/ min

Speed of Shyam

= 27/30

= 0.9 Km/min

Shyam drives faster.

**Question no – (7)**

**Solution :**

7 min = 7/60 hour

So, speed of the runner

= 3.5/7/60

=35/10 x 60/7

= 30 Km/h

**Question no – (8)**

**Solution :**

New Delhi Howrah Speed

= 1440/18

= 80 Km/h

New Delhi Vadodara speed

= 1020/12

= 85 Km/h

**Ratio, Proportion and Unitary Method Exercise 8E Solution :**

**Question no – (1)**

**Solution :**

As the auto rickshaw stops for 2 hours.

So, the 2 hours is not to be Counted,

So, the Average speed

= 380/10

= 38 Km/h

**Question no – (2)**

**Solution :**

Total distance

= 294 Km

8 am to 2 Pm

= (4 + 2)

= 6 hour

1 hour 20 min

= 80/60

= 4/3 hour

If the bus non-stop, then average sped

= 294/6

= 49 Km/h

If take rest, so time

= 6 – 4/3

= 18 – 4/3

= 14/3 hour

Then speed,

= 294/14 × 3

= 63 Km/h

**Question no – (3)**

**Solution :**

Distance = 220 km

Time = 0900 hour to 1400

= 5 hour 2h 30 m 2 + 30/60

= 2.5 hour

The speed = 220/5

= 44 Km/h

If steps of 2.30 min

So, time = 5 – 2.50

= 2.50 min

Then Speed = 220/2.5

= 220/25 x 10

= 88 Km/h

**Ratio, Proportion and Unitary Method Exercise 8F Solution :**

**Question no – (1)**

**Solution :**

**(a) 72 km/h**

= 72 × 1000/ 60 × 60

= 20 m/s

**(b) 45 km/h**

= 45 × 1000/ 60 × 60

= 50/104

= 12.5 m/s

**(c) 108 km/h**

= 108 × 1000/ 60 × 60

= 30 m/s

**Question no – (2) **

**Solution :**

**(a) 36 km/h**

= 36 × 1000/60

= 600 m/min

**(b) 75 km/h**

= 75 × 1000/60

= 1250 m/ min

**(c) 63 km/h**

= 63 × 1000/ 60

= 1050 m/min

**Question no – (3) **

**Solution :**

**(a)** Speed

= 30 × 1/1000/ 1 × 1/3600

= 30 × 3600/1000

= 108 km/h

**(b)** Speed

= 45 × 1/1000/1 × 3600

= 270/100

= 2.7 km/h

**(c)** Speed

= 12.5 × 1/1000/1× 1/3600

= 125/10 × 1/1000 × 3600

= 4500/100

= 45 km/h

**Question no – (4)**

**Solution :**

Speed

= 60 × 1000/3600

= 16.6 m/s

**Question no – (5)**

**Solution :**

Speed

= 15 m/s

= 15 × 1/1000/1/3600

= 15 × 3600/1000

= 540/10

= 54 km/h

**Ratio, Proportion and Unitary Method Exercise 8G Solution :**

**Question no – (1) **

**Solution :**

Speed : |
Distance : |
Time : |

(a) 21 km/h |
(21 × 3) = 63 km | 3 hour |

(b) 45 km/h |
630 km | 630/45 = 14 hour |

(c) 25 m/s |
450 m | 450/25 = 18s |

(d) 56 m/s |
(56 × 15) = 840 m | 15s |

(e) 15m/min |
345m | 345/15 = 23 minutes. |

**Question no – (2)**

**Solution :**

Distance

= 54 × 3

= 162 km.

**Question no – (3)**

**Solution :**

The bus take time

= 192/48

= 4 h.

**Question no – (4)**

**Solution :**

3 hour 20 mint

= 3 +20/60

= 3 + 3/1

= 10/3

Far of the destination

= 10/3 × 18/54

= 180 km

**Question no – (5)**

**Solution :**

12 min

= 12/60 hour

So, Distance he cover

= 12 × 12/60

= 24/10

= 2.4 km

**Question no – (6)**

**Solution :**

375 m

= 375/1000km

So, the man take time

= 375 ÷ 15

= 375/1000 × 1/15

= 25/1000

= 0.025 h

= 0.025 × 60

= 1.5 min

**Question no – (7)**

**Solution :**

6.30 am → 7.00 pm

Time = 12 hour 30 mint

= 12.5 hour

So, average distance

= 12.5 × 80

= 1000 km

**Question no – (8)**

**Solution :**

The aero plane take time

= 1500/600

= 5/2

= 2.5 hour.

= 2 hour 30 mint

**Question no – (9)**

**Solution :**

10m/s = 10 × 1/1000/1/3600

= 36 km /h

So, time = 6/36 hour

= 6/36 × 60

= 10 minutes

**Next Chapter Solution : **

👉 Chapter 9 👈