**Ratio and Proportion**** Class 6 Ex. 12.2**

**Ratio and Proportion, Ncert Class 6, Chapter 12, Exercise 12.2 Math Free Solution.**

**Exercise 12.2**

**Question 1 :- Determine, if the following are in proportion.**

**(a) 15, 45, 40, 120**

**(b) 33, 121, 9, 96**

**(c) 24, 28, 36, 48**

**(d) 32, 48, 70, 210**

**(e) 4, 6, 8, 12**

**(f) 33, 44, 75, 100**

**Solution 1:- **

(a)

Since, 15 : 45 : : 40 : 120

So, 15, 45, 40 and 120 **are in proportion.**

(b)

Since, 33 : 121 not equal to 9 : 96

So, 33, 121, 9, and 96 **not in proportion.**

(c)

Since, 24 : 48 not equal to 36 : 48

So, 24, 28, 36, and 48 **not in proportion.**

(d)

Since, 32 : 48 not equal to 70 : 210

So, 32, 48, 70, and 210 **not in proportion.**

(e)

Since, 4 : 6 : : 8 : 12

So, 4, 6, 8 and 12** are in proportion.**

(f)

Since, 33 : 44 : : 75 : 100

So, 33, 44, 75 and 100** are in proportion.**

**Question 2 :- Write True (T) or False (F) against each of the following statements:**

**(a). 16 : 24 : : 20 : 30; **

**(b). 21 : 6 : : 35 : 10;**

**(c). 12 : 18 : : 28 : 12;**

**(d). 8 : 9 : : 24 : 27;**

**(e). 5.2 : 3.9 : : 3 : 4;**

**(f). 0.9 : 0.36 : : 10 : 4;**

**Solution 2:-**

(a). 16 : 24 : : 20 : 30;

Product of the external terms = 16 x 30 = 480

Product of the internal terms = 24 x 20 = 480

So, The given statement (a) is **True.**

(b). 21 : 6 : : 35 : 10;

Product of the external terms = 21 x 10 = 210

Product of the internal terms = 6 x 35 = 210

So, The given statement (b) is **True.**

(c). 12 : 18 : : 28 : 12;

Product of the external terms = 12 x 12 = 144

Product of the internal terms = 18 x 28 = 504

Since 144 ≠ 504 or 12 : 18 not equals to 28 : 12

So, The given statement (c) is **False.**

(d). 8 : 9 : : 24 : 27;

The product of the external terms = 8 x 27 = 216

The product of the internal terms = 9 x 24 = 216

So, the given statement (d) is **True.**

(e). 5.2 : 3.9 : : 3 : 4;

Product of the extreme terms = 5.2 x 4 = 20.8

Product of the middle terms = 3.9 x 3 = 11.7

Since, 20.8 ≠ 11.7 or 5.2 : 3.9 not equals to 3 : 4

So, the given statement (e) is **False.**

(f). 0.9 : 0.36 : : 10 : 4;

Product of the external terms = 0.9 x 4 = 3.6

Product of the internal terms = 0.36 x 10 = 3.6

Since, 3.6 = 3.6 or 5.2 : 3.9 not equals to 3 : 4

So, the given statement (f) is **True.**

**Question 3 :- Are the following statements true?**

**(a). 40 persons : 200 persons = ₹15 : ₹75;**

**(b). 7.5 litres : 15 litres = 5 kg : 10 kg;**

**(c). 99 kg : 45 kg = ₹ 44 : ₹ 20;**

**(d). 32 m : 64 m = 6 sec : 12 sec;**

**(e). 45 km : 60 km = 12 hours : 15 hours;**

**Solution 3:-**

(a). 40 persons : 200 persons =

₹15 : ₹75 =

Since, 40 persons : 200 persons = ₹15 : ₹75

So, the statement (a) is **True.**

(b) 7.5 litres : 15 litres =

5kg : 10kg =

Since, 7.5 litres : 15 litres = 5 kg : 10 kg

So, the statement (b) is **True.**

(c) 99 kg : 45 kg =

₹ 44 : ₹ 20 =

Since, ratios are equal :- 99 kg : 45 kg = ₹ 44 : ₹ 20;

So, the statement (c) is **True.**

(d) 32 m : 64 m =

6 sec : 12 sec =

Since, ratios are equal :- 32 m : 64 m = 6 sec : 12 sec

So, the statement (d) is **True.**

(e). 45 km : 60 km = 12 hours : 15 hours;

12 hours : 15 hours =

Since, 45 km : 60 km = 12 hours : 15 hours

So, the statement (e) is not true.

**Question 4 :- Determine; if the following ratio form a proportion. Also, write the middle-terms and extreme-terms; where the ratios form a proportion.**

**(a) 25cm : 1m and ₹40 : ₹160**

**(b) 39-litres : 65-litres and 6-bottles : 10-bottles;**

**(c) 2kg : 80kg and 25g : 625g**

**(d) 200mL : 2.5 litres and ₹4 : ₹50**

**Solution 4:- **

(a) 25cm : 1m = 25cm : 100cm ; [ Since, 1 m = 100 cm ]

25/100 = 1/4 = 1 : 4; and

| ₹40 : ₹160 = 40/160 = 1/4 = 1 : 4;

So, the given ratios are** in proportion**.

**.Extreme-terms** are 25 cm and ₹ 160;

**Middle terms** are 1 m and ₹40.

(b) 39 litres : 65 litres =

39/65 = (39/13)/(65/13) = 3/5 = 3 : 5; and

6 bottle : 10 bottle = 6/10 = 3/5 = 3 : 5;

So, the given ratios are** in proportion**.

**Extreme terms** are 39 litres and 10 bottle.

**Middle terms** are 65 litres and 6 bottle.

(c) 2 kg : 80 kg =

2/80 = 1/40 = 1 : 40; and

25g : 625g = 25/625 = 1/5 = 1 : 5;

Since, the ratio are not equal

So, the given ratios are** not in proportion**.

**Extreme terms** are 2 kg and 625 g.

**Middle terms** are 80 kg and 25 g.

(d) 200 ml : 2.5 litres = 200ml : 2500 ml [ Since, 1 litres = 1000 ml ]

200/2500 = 2/25 = 2 : 25; and

₹ 4 : ₹ 50 = 4/50 = 2/25 = 2 : 25;

Since, the ratio are equals

So, the given ratios are in proportion.

**Extreme terms** are 200 ml and ₹ 50.

**Middle terms** are 2.5 litres and ₹ 4.

**Chapter 12 Ratio and Proportion Class 6 Exercise. 12.2 for Free.**