**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

**Answer**:

(a) 15, 45, 40, 120

Therefore, 15: 45 = 40: 120

Hence, these are in proportion.

(b) 33, 121, 9, 96

Therefore, 33: 121 ≠ 9: 96

Hence, these are not in proportion.

(c) 24, 28, 36, 48

Therefore, 24: 28 ≠ 36: 48

Hence, these are not in proportion.

(d) 32, 48, 70, 210

Therefore, 32: 48 ≠ 70: 210

Hence, these are not in proportion.

(e) 4, 6, 8, 12

Therefore, 4: 6 = 8: 12

Hence, these are in proportion.

(f) 33, 44, 75, 100

Therefore, 33: 44 = 75: 100

Hence, these 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

**Answer**:

(a) 16: 24:: 20: 30

Therefore, 16: 24 = 20: 30

Hence, True

(b) 21: 6:: 35: 10

Therefore, 21: 6 = 35: 10

Hence, True

(c) 12: 18:: 28: 12

Therefore, 12: 18 ≠ 28: 12

Hence, False

(d) 8: 9:: 24: 27

As ,

Therefore, True

(e) 5.2: 3.9:: 3: 4

As ,

Therefore, 5.2: 3.9 ≠ 3: 4

Hence, False

(f) 0.9: 0.36:: 10: 4

Therefore, 0.9: 0.36 = 10: 4

Hence, True

**Question** 3:

Are the following statements true?

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

(b) 7.5 litres: 15 litres = 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 = Rs 15: Rs 75

True

(b) 7.5 *l*: 15 *l* = 5 kg: 10 kg

True

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

True

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

True

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

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 litres: 65 litres and 6 bottles: 10 bottles

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

(d) 200 mL: 2.5 litre and Rs 4: Rs 50

**Answer**:

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

25 cm = = 0.25 m

Yes. These are in proportion.

Middle terms are 1m, Rs 40.

Extreme terms are 25 cm, Rs 160.

(b) 39 *l*: 65 *l *and 6 bottles: 10 bottles

Yes. These are in proportion.

Middle terms are 65 *l*, 6 bottles.

Extreme terms are 39 *l*, 10 bottles.

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

No. These are not in proportion.

(d) 200 mL: 2.5 *l* and Rs 4: Rs 50

1* l* = 1000 mL

2.5* l* = 2500 mL

Yes. These are in proportion.

Middle terms are 2.5 *l*, Rs 4.

Extreme terms are 200 mL, Rs 50.