**ML Aggarwal CBSE Solutions Class 6 Math 9th Chapter Ratio and Proportion Exercise 9.1**

**Ex. 9.1**

**(1) Express the following ratios in simplest form:**

(i) 20 : 40

**Solution:** = 1 : 2

(ii)40 : 20

**Solution: **2 : 1

(iii) 81 : 108

**Solution: **9 : 12

= 3 : 4

(iv) 98 : 63

**Solution: **14 : 9

**(2) Fill in the missing numbers in the following equivalent ratios:**

**(3) Find the ratio of each of the following in simplest form:**

**(i) 2.1 m to 1.2 m**

**Solution: **2.1: 1.2

= 21/10 : 12/20

= 21 : 12

= 7 : 4

**(ii) 91 cm to 1.04 m**

**Solution: **1.04 m = 104 cm

Now, 91 cm : 104 cm

= 7 : 8

**(iii) 3.5 kg to 250 g**

**Solution: **3.5 kg = 3500 g

Now, 3500 g : 250 g

= 700 : 50

= 140 : 10

= 28 : 2

= 14 : 1

**(iv) 60 paise to 4 rupees**

**Solution: **4 rupees = 400 paise

Now, 60 : 400

= 15 : 100

= 3 : 20

**(v) 1 minute to 15 seconds**

**Solution: **1 minute = 60 seconds

Now, 60 : 15

= 4 : 1

**(vi) 15 mm to 2 cm**

**Solution: **2 cm = 20 mm

Now, 15 mm : 20 mm

= 3 : 4

**(4) The length and the breadth of a rectangular park are 125 m and 60 m respectively. What is the ratio of the length to the breadth of the park?**

**Solution: **The ration of the length to the breadth of the park = 125 m : 60 m

= 25 : 12

**(5) The population of village is 4800. If the number of females is 2160, find the ratio of the males to that of females.**

**Solution: **Total population of the village = 4800

Number of females = 2160

∴ Number of males = 4800 – 2160 = 2640

The ratio of the males to that of females = 2640 : 2160

= 528 : 432

= 264 : 216

= 132 : 108

= 66 : 54

= 33 : 27

= 11 : 9

**(6) In a class, there are 30 boys and 25 girls. Find the ratio of the number of**

**(i) boys to that of girls**

**(ii) girls to that of total number of students.**

**(iii) boys to that of total number of students.**

**Solution: **(i) boys to that of girls =

30 : 25

= 6 : 5

(ii) Total number of students = 30 + 25 = 55

The ratio of girls to that of total number of students = 25 : 55

= 5 : 11

(iii) Total number of students = 55

The ratio of boys to that of total number of students = 30 : 55

= 6 : 11

**(7) In a year, Reena earns Rs. 1,50,000 and saves Rs. 50,000. Find the ratio of**

**(i) money she earns to the money she saves**

**(ii) money that she saves to the money she spends.**

**Solution: **Reena earns = 1,50,000

She saves = 50,000

That’s mean, she spends 1,50,000 – 50,000 = 1,00,000

(i) The ratio of money she earns to the money she saves = ** **1,50,000 : 50,000

= 30000 : 10000

= 6000 : 2000

= 3 : 1

(ii) The ratio of money that she saves to the money that she spends =

50,000 : 1,00,000

= 1 : 2

**(8) The monthly expenses of a student have increased from Rs. 350 to Rs. 500. Find the ratio of **

**(i) increase in expenses to original expenses**

**(ii) original expenses to increased expenses**

**(iii) increased expenses to increase in expenses**

**Solution: **Increase in expenses = 500 – 350 = 150

(i) The ratio of increase in expenses to original expenses = 150 : 350

= 30 : 70

= 6 : 14

= 3 : 7

(ii) original expenses to increased expenses = 350 : 500

= 70 : 100

= 14 : 20

= 7 : 10

(iii) The ratio of increased expenses to increase in expenses = 500 : 150

= 100 : 30

= 50 : 15

= 10 : 3

**(9) Mr Mahajan and his wife are both school teachers and earn Rs. 20900 and Rs. 18700 per month respectively. Find the ratio of:**

**(i) Mr Mahajan’s income to his wife’s income**

**(ii) Mrs Mahajan’s income to the total income of both**

**Solution: **Mr Mahajan’s income = Rs. 20900

Mrs. Mahajan income = Rs. 18700

Their total income = 20900 + 18700

= 39600

(i) The ratio of Mr Mahajan’s income to his wife income = 20900 : 18700

= 4180 : 3740

= 836 : 748

= 418 : 374

= 209 : 187

(ii) The ratio of Mrs Mahajan income to the total income of both =

18700 : 39600

= 3720 : 7920

= 744 : 1584

= 372 : 792

= 186 : 396

= 93 : 198

**(10) Out of 30 students in a class, 6 like football, 12 like cricket and remainining likes tennis. Find the ratio of**

**(i) number of students liking football to number of students liking tennis.**

**(ii) number of students liking cricket to total number of students.**

**Solution: **Total students = 30

Number of students like football = 6

Number of students like cricket = 12

Number of students like tennis = 30 – (6 + 12)

= 30 – 18

= 12

**(11) Divide Rs. 560 between Ramu and Munni in the ratio 3 : 2**

**Solution: **Total Rs. 560

Ramu get = 560 x 3/5

= 112 x 3

= 336

Munni get = 560 x 2/5

= 112 x 2

= 224

**(12) Two people invested Rs. 15000 and Rs. 25000 respectively to start a business. They decided to share the profits in the ratio of their investments. If their profit is Rs. 12000, how much does each get.**

**Solution: **Total investment = 15000 + 25000 = 40000

1^{st} people get in profit = 12000 x 15000/40000

= 3 x 1500

= 4500

2nd people get in profit = 12000 x 25000/40000

= 7500

**(13) The ratio of Ankur’s money to Roma’s is 9 : 11. If Ankur has Rs. 540, how much money does Roma have?**

**Solution: **Let, the total money be x

Ankur has Rs. 540

Therefore,

X x 9/20 = 540

9x/20 = 540

=> 9x = 10800

=> x = 10800 / 9

=> x = 1200

∴ Roma get = 1200 – 540

= 1160

**(14) The ratio of weights of tin and zinc in an alloy is 2:5. How much zinc is there in 31.5 of alloy?**

**Solution: **The ratio of weights of tin and zinc in an alloy is 2:5

Tin have = 2/7

Zinc have = 5/7

∴ zinc have in an alloy = 31.5 x 5/7

= 315/10 x 5/7

= 22.5 g