Ratio and Proportion-Solutions Ex-12.2

CBSE Class –VI Mathematics
NCERT Solutions
Chaper 12 Ratio And Proportion (Ex. 12.2)

---

Question 1. Determine 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

Answer: (a) 15 : 45 =  1 : 3

40 : 120 =  1 : 3

Since 15 : 45 = 40 : 120

Therefore 15, 45, 40, 120 are in proportion.

(b) 33 : 121 =  3 : 11

9 : 96 =  3 : 32

Since 33 : 121 ≠$\ne$ 9 : 96

Therefore, 33, 121, 9, 96 are not in proportion.

(c) 24 : 28 =  6 : 7

36 : 48 =  3 : 4

Since 24 : 28 ≠$\ne$ 36 : 48

Therefore 24, 28, 36, 48 are not in proportion.

(d) 32 : 48 = 2 : 3

70 : 210 =  1 : 3

Since 32 : 48 ≠$\ne$ 70 : 210

Therefore 32, 48, 70, 210 are not in proportion.

(e) 4 : 6 =  2 : 3

8 : 12 =  2 : 3

Since 4 : 6 = 8 : 12

Therefore 4, 6, 8, 12 are in proportion.

(f) 33 : 44 =  3 : 4

75 : 100 =  3 : 4

Since 33 : 44 = 75 : 100

Therefore 33, 44, 75, 100 are in ratio.

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

Answer: (a) 16 : 25 : : 20 : 30 ⇒$\Rightarrow$ ⇒$\Rightarrow$23=23$\frac{2}{3}=\frac{2}{3}$

Hence, it is True.

(b) 21 : 6 : : 35 : 10 ⇒$\Rightarrow$ ⇒$\Rightarrow$72=72$\frac{7}{2}=\frac{7}{2}$

Hence, it is True.

(c) 12 : 18 : : 28 : 12 ⇒$\Rightarrow$ ⇒$\Rightarrow$23≠73$\frac{2}{3}\ne \frac{7}{3}$

Hence, it is False.

(d) 8 : 9 : : 24 : 27 ⇒$\Rightarrow$ ⇒$\Rightarrow$89=89$\frac{8}{9}=\frac{8}{9}$

Hence, it is True.

(e) 5.2 : 3.9 : : 3 : 4 ⇒$\Rightarrow$ ⇒$\Rightarrow$43≠34$\frac{4}{3}\ne \frac{3}{4}$

Hence, it is False.

(f) 0.9 : 0.36 : : 10 : 4 ⇒$\Rightarrow$ ⇒$\Rightarrow$52=52$\frac{5}{2}=\frac{5}{2}$

Hence, it is True.

Question 3. Are the following statements true:

(a) 40 persons : 200 persons = Rs. 15 : Rs. 75

(b) 7.5 liters : 15 liters = 5 kg = 10 kg

(c) 99 kg : 45 kg = Rs. 44 : Rs. 20

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

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

Answer: (a) 40 persons : 200 persons :: 1 : 5

Rs. 15 : Rs. 75 = = 1 : 5

Since, 40 persons : 200 persons = Rs. 15 : Rs. 75

Hence, the statement is true.

(b) 7.5 liters : 15 liters = = 1 : 2

5 kg : 10 kg = = 1 : 2

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

Hence, the statement is true.

(c) 99 kg : 45 kg = = 11 : 5

Rs. 44 : Rs. 20 = = 11 : 5

Since, 99 kg : 45 kg = Rs. 44 : Rs. 20

Hence, the statement is true.

(d) 32 m : 64 m = = 1 : 2

6 sec : 12 sec = = 1 : 2

Since, 32 m : 64 m = 6 sec : 12 sec

Hence, the statement is true.

(e) 45 km : 60 km = = 3 : 4

12 hours : 15 hours = = 4 : 5

Since, 45 km : 60 km ≠$\ne$ 12 hours : 15 hours

Hence, the statement is false.

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

(a) 25 cm : 1 m and Rs. 40 : Rs. 160

(b) 39 liters : 65 liters and 6 bottles : 10 bottles

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

(d) 200 ml : 2.5 ml and Rs. 4 : Rs. 50

Answer: (a) 25 cm : 1 m = 25 cm : (1 x 100) cm = 25 cm : 100 cm = = 1 : 4

Rs. 40 : Rs. 160 = = 1 : 4

Since the ratios are equal, therefore these are in proportion.

Middle terms = 1 m, Rs. 40 and Extreme terms = 25 cm, Rs. 160

(b) 39 liters : 65 liters = 3 :5

6 bottles : 10 bottles = = 3 : 5

Since the ratios are equal, therefore these are in proportion.

Middle terms = 65 liters, 6 bottles and Extreme terms = 39 liters, 10 bottles

(c) 2 kg : 80 kg = = 1 : 40

25 g : 625 g = = 1 : 25

Since the ratios are not equal, therefore these are not in proportion.

(d) 200 ml : 2.5 liters = 200 ml : (25 x 1000) liters = 200 ml : 2500 ml = = 2 : 25

Rs. 4 : Rs. 50 = = 2 : 25

Since the ratios are equal, therefore these are in proportion.

Middle terms = 2.5 liters, Rs. 4 and Extreme terms = 200 ml, Rs. 50