ML Aggarwal CBSE Solutions Class 6 Math Ninth Chapter Ratio and Proportion Exercise 9.1

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

1st 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


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