**Comparing Quantities(Ratio)**

Ratio of Circumference: Diameter = π image credits: openclipart |

**Important Points**

*. In the ratio x:y (called as x is to y), x is called the*

**1***or*

__first term__*. y is called the*

__antecedent__*or*

__second term__*.*

__consequent__*. While comparing two quantities, the units must be the same.*

**2***. A ratio remains unchanged if both its terms are multiplied or divided by same non-zero number.*

**3***. The ratio (p:q) is said to be in simplest form when HCF of p and q is 1.*

**4****NCERT Exercise 8.1**

**Q1: Find the ratio of:**

**(a) ₹ 5 to 50 paise**

**(b) 15 kg to 210 g**

**(c) 9 m to 27 cm**

**(d) 30 days to 36 hours**

Answer:

(a) ₹ 5 to 50 paise

Since units are not same, we need to convert both to same units.

∵ ₹ 1 = 100 paise ∴ ₹ 5 = 5 × 100 = 500 paise

∴ ₹ 5 to 50 paise = 500 paise: 50 paise = 500/50 =

**10:1**

(b) 15 kg to 210 g

Since units are not same, we need to convert both to same units.

∵ 1 kg = 1000g ∴ 15kg = 15 × 1000 = 15000g

∴ 15 kg to 210 g = 15000g : 210g = 15000/210 =

**500:7**

(c) 9 m to 27 cm

Converting both terms to same units.

∵ 1m = 100 cm ∴ 9m = 9 × 100cm = 900cm

∴ 9m to 27cm = 900cm : 27cm = 900 / 27 = 100/3 =

**100:3**

(d) 30 days to 36 hours

Converting both terms to same units.

∵ 1 day = 24 hours

∴ 30 days = 30 × 24 hours = 720 hours

∴ 30 days to 36 hours = 720 hours : 36 hours =720/36 = 20/1 =

**20:1**

**Q2: In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?**

Answer:

**Q3:Population of Rajasthan = 570 lakhs and population of UP = 1660 lakhs.**

**Area of Rajasthan = 3 lakh km**

^{2}and area of UP = 2 lakh km^{2}.**(i) How many people are there per km**

^{2}in both these States?**(ii) Which State is less populated?**

Answer:

Let us calculate ratio as population per area.

Population of Rajasthan per 3 lakh km

^{2}= 570 lakh

Population of Rajasthan per 1 lakh km

^{2}=570/3 = 190 lakh ... (I)

Population of UP per 2 lakh km

^{2}= 1660 lakh

Population of UP per 1 lakh km

^{2}= 1660/2 = 830 lakh ...(II)

Comparing values I and II, we can say population ratio per area of Rajasthan is less.

**Other Questions on Ratio**

**Q4: Express 24:30 in its simplest form.**

Answer: Ratio in simplest form is when HCF of two terms is 1 i.e. there is no common factor except one.

∴ 24 : 30 = 4 × 2 × 3 : 5 × 2 × 3 =

**4 : 5**

**Q5: Express ratio 1m 5cm : 63 cm in simplest form.**

Answer: Converting into same units.

∵ 1m = 100 cm

∴ 1m 5cm = 100 cm + 5 cm = 105 cm

∴ 1m 5cm : 63 cm = 105 cm : 63 cm = 7 × 5 × 3 : 7 × 3 × 3 =

**5 : 3**

**Q6: Divide ₹ 360 in the ratio 7:8.**

Answer: Let the two values after division is 7x and 8x.

Sum of these values = 7x + 8x = 15x = ₹ 360

⇒ x = 360/15 = 24

∴ First value = 7x = 7 × 24 = ₹ 168

and the second value = 8x = 8 × 24 = ₹ 192

Thus ₹360 is divided into ₹168 and ₹192 as per the given ratio (7:8)

**Q7: Two numbers are in the ratio of 7:11. If 7 is added to each of the numbers the ratio becomes 2:3. Find the numbers.**

Answer:

Let the first number = 7p

and the second number = 11p

After adding 7, the first number becomes = 7p + 7

After adding 7, the second number becomes = 11p + 7

The new ratio is,

Thus numbers are 49 and 77.

**Q8: If 15 oranges cost Rs 70, what do 39 oranges cost?**

Answer: Cost of 15 oranges = ₹70

Cost of 1 orange = 70/15

Cost of 39 oranges = 70 × 39 /15 = 14 ×

**13 =**

**₹182**

**Q9: Fill in the blanks:**

- The comparison of two quantities of the same kind by means of division is termed as_____________.
- The two quantities to be compared are called the ________ of the ratio.
- The first term of the ratio is called the _________ and the second term is called the _______.
- Equality of two ratios is called a __________. If a,b;c,d are in proportion,then a:b::c:d .
- In a proportion, the product of extremes =___________

- ratio
- terms
- antecedent, consequent
- proportion
- product of means

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