Chapter 8: Ratio and Proportion

Solution:-

True

Consider the two ratios 27cm² : 57cm² = 18cm : 38cm

27/57 = 18/38

27/57 is further simplified by dividing both the numerator and denominator by 3 we get,

= 9/19

18/38 is further simplified by dividing both the numerator and denominator by 2, and we get,

= 9/19

Hence, 9/19 = 9/19

Therefore, 27cm² : 57cm² = 18cm : 38cm

Solution:-

False.

Consider the two ratios 5kg: 7.5kg = Rs 7.50: Rs 5

5/7.5 = 7.50/5

50/75 = 75/50

50/75 is further simplified by dividing both the numerator and denominator by 25 we get,

= 2/3

75/50 is further simplified by dividing both the numerator and denominator by 25 we get,

= 3/2

Hence, 2/3 ≠ 3/2

Therefore, 5kg: 7.5kg ≠ Rs 7.50: Rs 5

Solution:-

True

Consider the given ratios, 20g : 100g = 1 metre : 500cm

20/100 = 1/500

We know that, 1 metre = 100 cm

So, 20g: 100g = 100cm : 500 cm

20/100 = 100/500

20/100 is further simplified by dividing both the numerator and denominator by 20 we get,

= 1/5

100/500 is further simplified by dividing both the numerator and denominator by 100 we get,

= 1/5

Hence, 1/5 = 1/5

Therefore, 20g : 100g = 1metre: 500cm

Solution:-

True

Consider the given ratios, 12 hours : 30 hours = 8km : 20km

12/30 = 8/20

12/30 is further simplified by dividing both the numerator and denominator by 6 we get,

= 2/5

8/20 is further simplified by dividing both the numerator and denominator by 4 we get,

= 2/5

Hence, 2/5 = 2/5

Therefore, 12 hours : 30 hours = 8km : 20km

Solution:-

True.

The ratio of 10kg to 100kg = 10/100

= 1/10

= 1:10

Solution:-

False

We know that, 1 metre = 100 cm

So, the ratio of 150cm to 1metre is = 150/100

= 15/10

Divide both the numerator and denominator by 5 we get,

= 3/2

So, the ratio of 150cm to 1metre is 3: 2

Solution:-

True.

We know that, 1 kg = 1000 g

So, 25 × 1000 = 25000 g

50 × 1000 = 50000g

Then, 25000g : 20g = 50000g : 40g

25000/20 = 50000/40

2500/2 = 5000/4

2500/2 is further simplified by dividing both the numerator and denominator by 2 we get,

= 1250

5000/4 is further simplified by dividing both the numerator and denominator by 4, and we get,

= 1250

Hence, 1250 = 1250

So, 25kg : 20g = 50kg : 40g

Solution:-

False

We know that, 1 day = 24 hours

So, 1 hour: 1 day = 1 hour : 24 hours

1/1 ≠ 1/24

Solution:-

False

4 : 16

= 4/16

Divide both numerator and denominator by 4,

= 1/4

Therefore, the lowest form of 4: 16 is 1/4

Solution:-

True.

5: 4 ≠ 4: 5

5/4 ≠ 4/5

1.25 ≠ 0.8