{"id":2152,"date":"2020-12-06T11:12:29","date_gmt":"2020-12-06T11:12:29","guid":{"rendered":"https:\/\/themindpalace.in\/?p=2152"},"modified":"2021-08-26T05:34:08","modified_gmt":"2021-08-26T05:34:08","slug":"ratio-and-proportion","status":"publish","type":"post","link":"https:\/\/themindpalace.in\/index.php\/2020\/12\/06\/ratio-and-proportion\/","title":{"rendered":"Ratio and Proportion"},"content":{"rendered":"\n

Summary of ratio and proportion<\/a><\/p>\n\n\n\n

Solved exercise of ration and proportion<\/a><\/p>\n\n\n\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Summary<\/h1>\n\n\n\n

Ratio:<\/span> We compare two quantities. This comparison is known as the ratio.<\/p>\n\n\n\n

Ratio is denoted by symbol <\/span>:<\/strong><\/span><\/p>\n\n\n\n

Example: <\/span>T<\/span>he ratio of the cost of a pen to the cost of a pencil =10\/5=5\/1=5:1<\/p>\n\n\n\n

Two quantities can be compared only if there are in the same unit.<\/p>\n\n\n\n

Example: The length of the lizard is 20.<\/p>\n\n\n\n

The length of crocodile is 400<\/p>\n\n\n\n

Therefore the ratio of the length of lizard and crocodile is 20\/400=1\/20=1:20<\/p>\n\n\n\n

Here two ratio 1:20 and 20:1 are different from each other . The ratio 1:20 is the ratio of the length of the lizard and 20:1 is the ratio length of crocodile.<\/p>\n\n\n\n

Proportion:<\/span><\/strong>I<\/span>f two ratio are equal we say that they are in proportion and use the symbol :: or= to equate the two ratio. <\/p>\n\n\n\n

Example:<\/span><\/strong> 3,10,15,and 50 are in proportion written as 3:10::15:50<\/p>\n\n\n\n

If two ratios are not equal then we say that they are not in proportion. It is a statement of proportion the four quantities involved when taken in order are known as respective terms.The first 4 terms are known as extreme terms.2nd and 3rd terms are known as middle terms.<\/p>\n\n\n\n

Example: Are 30, 40, 45,and 60 in proportion?<\/p>\n\n\n\n

Ratio of 30 to 40=30\/40=3:4<\/p>\n\n\n\n

Ratio of 45 to 60 =45\/60=3:4<\/p>\n\n\n\n

Since 30:40=45:60<\/p>\n\n\n\n

therefore 30,40,45,60 are in proportion.<\/p>\n\n\n\n

Unitary Method<\/span><\/strong><\/p>\n\n\n\n

The method in whihc first we find the value of one unit and then the value of required number of unit is known as unitary method.<\/p>\n\n\n\n

Example<\/span><\/strong>: If cost of 6 cans of juice is rs 210 then what will be the cost of 4 cans of juice?<\/p>\n\n\n\n

Cost of 6 cans of juice =Rs 210<\/p>\n\n\n\n

The cost of one can of juice =210\/635<\/p>\n\n\n\n

thereforecost of 4 can of juice =35×4=140<\/p>\n\n\n\n

Cost of 4 can of juice is Rs 140<\/span><\/strong><\/p>\n\n\n\n

Exercise 12.1<\/span><\/h1>\n\n\n\n

1. There are 20 girls and 15 boys in a class.<\/strong><\/p>\n\n\n\n

(a) What is the ratio of number of girls to the number boys?<\/strong><\/p>\n\n\n\n

(b) What is the ratio of number of girls to the total number of students in the class?<\/strong><\/p>\n\n\n\n

Solutions:<\/span><\/strong><\/p>\n\n\n\n

Given<\/p>\n\n\n\n

Number of girls = 20 girls<\/p>\n\n\n\n

Number of boys = 15 boys<\/p>\n\n\n\n

Total number of students = 20 + 15<\/p>\n\n\n\n

= 35<\/p>\n\n\n\n

Ratio of number of girls to number of boys = 20 \/ 15 = 4 \/ 3<\/p>\n\n\n\n

(b) Ratio of number of girls to total number of students = 20 \/ 35 = 4 \/ 7<\/p>\n\n\n\n

\n\n\n\n

2. Out of 30 students in a class, 6 like football, 12 like cricket and remaining like tennis. Find the ratio of<\/strong><\/p>\n\n\n\n

(a) Number of students liking football to number of students liking tennis.<\/strong><\/p>\n\n\n\n

Solutions:<\/strong><\/p>\n\n\n\n

Given<\/p>\n\n\n\n

Number of students who like football = 6<\/p>\n\n\n\n

Number of students who like cricket = 12<\/p>\n\n\n\n

Number of students who like tennis = 30 \u2013 6 \u2013 12<\/p>\n\n\n\n

= 12<\/p>\n\n\n\n

\n\n\n\n

(a) Ratio of number of students liking football to the number of students liking tennis<\/p>\n\n\n\n

= 6 \/ 12 = 1 \/ 2<\/p>\n\n\n\n

\n\n\n\n

(b) Ratio of number of students liking cricket to total number of<\/p>\n\n\n\n

= 12 \/ 30<\/p>\n\n\n\n

= 2 \/ 5<\/p>\n\n\n\n

\n\n\n\n

3. See the figure and find the ratio of<\/strong><\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

(a) Number of triangles to the number of circles inside the rectangle.<\/strong><\/p>\n\n\n\n

Solutions:<\/strong><\/p>\n\n\n\n

Given in the figure<\/p>\n\n\n\n

Number of triangles = 3<\/p>\n\n\n\n

Number of circles = 2<\/p>\n\n\n\n

Number of squares = 2<\/p>\n\n\n\n

Total number of figures = 7<\/p>\n\n\n\n

(a) Ratio of number of triangles to the number of circles inside the rectangle<\/p>\n\n\n\n

= 3 \/ 2<\/p>\n\n\n\n

\n\n\n\n

(b) Number of squares to all the figures inside the rectangle.<\/strong><\/p>\n\n\n\n

Ratio of number of squares to all the figures inside the rectangle<\/p>\n\n\n\n

= 2 \/ 7<\/p>\n\n\n\n

\n\n\n\n

(c) Number of circles to all the figures inside the rectangle.<\/strong><\/p>\n\n\n\n

Ratio of number of circles to all the figures inside the rectangle<\/p>\n\n\n\n

= 2 \/ 7<\/p>\n\n\n\n

\n\n\n\n

4. Distance travelled by Hamid and Akhtar in an hour are 9 km and 12 km. Find the ratio of speed of Hamid to the speed of Akhtar.<\/strong><\/p>\n\n\n\n

Solutions:<\/strong><\/p>\n\n\n\n

We know that the speed of a certain object is the distance travelled by that object in an hour<\/p>\n\n\n\n

Distance travelled by Hamid in one hour = 9 km<\/p>\n\n\n\n

Distance travelled by Akhtar in one hour = 12 km<\/p>\n\n\n\n

Speed of Hamid = 9 km\/hr<\/p>\n\n\n\n

Speed of Akhtar = 12 km\/hr<\/p>\n\n\n\n

Ratio of speed of Hamid to the speed of Akhtar = 9 \/ 12 = 3 \/ 4<\/p>\n\n\n\n

\n\n\n\n

5. Fill in the following blanks:<\/span><\/strong><\/p>\n\n\n\n

15 \/ 18 <\/strong>= \u2610 \/ 6 = 10 \/ \u2610 = \u2610 \/ 30 [Are these equivalent ratios?]<\/strong><\/p>\n\n\n\n

Solutions:<\/strong><\/p>\n\n\n\n

15 \/ 18 = (5 \u00d7 3) \/ (6 \u00d7 3)<\/p>\n\n\n\n

= 5 \/ 6<\/p>\n\n\n\n

5 \/ 6 = (5 \u00d7 <\/strong>2) \/ (6 \u00d7 2)<\/p>\n\n\n\n

= 10 \/ 12<\/p>\n\n\n\n

5 \/ 6 = (5 \u00d7 <\/strong>5) \/ (6 \u00d7 5)<\/p>\n\n\n\n

= 25 \/ 30<\/p>\n\n\n\n

Hence, 5, 12 and 25 are the numbers which come in the blanks respectively.<\/p>\n\n\n\n

Yes, all are equivalent ratios.<\/p>\n\n\n\n

\n\n\n\n

6. Find the ratio of the following:<\/strong><\/p>\n\n\n\n

(a) 81 to 108<\/strong><\/p>\n\n\n\n

(a) 81 \/ 108 = (3 \u00d7 <\/strong>3 \u00d7 3 \u00d7 3) \/ (2 \u00d7 <\/strong>2 \u00d7 3 \u00d7 3 \u00d7 3)<\/strong><\/p>\n\n\n\n

= 3 \/ 4<\/p>\n\n\n\n

\n\n\n\n

(b) 98 to 63<\/strong><\/p>\n\n\n\n

(b) 98 \/ 63 = (14 \u00d7 <\/strong>7) \/ (9 \u00d7 7)<\/p>\n\n\n\n

= 14 \/ 9<\/p>\n\n\n\n

\n\n\n\n

(c) 33 km to 121 km<\/strong><\/p>\n\n\n\n

(c) 33 \/ 121 = (3 \u00d7 <\/strong>11) \/ (11 \u00d7 11)<\/p>\n\n\n\n

= 3 \/ 11<\/p>\n\n\n\n

\n\n\n\n

(d) 30 minutes to 45 minutes<\/strong><\/p>\n\n\n\n

(d) 30 \/ 45 = (2 \u00d7 <\/strong>3 \u00d7 5) \/ (3 \u00d7 3 \u00d7 5)<\/p>\n\n\n\n

= 2 \/ 3<\/p>\n\n\n\n

\n\n\n\n

7. Find the ratio of the following:<\/span><\/strong><\/p>\n\n\n\n

(a) 30 minutes to 1.5 hours<\/strong><\/p>\n\n\n\n

(a) <\/strong>30 minutes to 1.5 hours<\/p>\n\n\n\n

30 min = 30 \/ 60<\/p>\n\n\n\n

= 0.5 hours<\/p>\n\n\n\n

Required ratio = (0.5 \u00d7 <\/strong>1) \/ <\/strong>(0.5 \u00d7 3)<\/p>\n\n\n\n

= 1 \/ 3<\/p>\n\n\n\n

\n\n\n\n

(b) 40 cm to 1.5 m<\/strong><\/p>\n\n\n\n

1.5 m = 150 cm<\/p>\n\n\n\n

Required ratio = 40 \/ 150 = 4 \/ 15<\/p>\n\n\n\n

\n\n\n\n

(c) 55 paise to \u20b9 1<\/strong><\/p>\n\n\n\n

\u20b9 1 = 100 paise<\/p>\n\n\n\n

Required ratio = 55 \/ 100 = (11 \u00d7 <\/strong>5) \/ (20 \u00d7 5)<\/p>\n\n\n\n

= <\/strong>11 \/ 20<\/p>\n\n\n\n

\n\n\n\n

(d) 500 ml to 2 litres<\/strong><\/p>\n\n\n\n

500 ml to 2 litres<\/p>\n\n\n\n

1 litre = 1000 ml<\/p>\n\n\n\n

2 litre = 2000 ml<\/p>\n\n\n\n

Required ratio = 500 \/ 2000 = 5 \/ 20 = 5 \/ (5 \u00d7 <\/strong>4)<\/p>\n\n\n\n

= <\/strong>1 \/ 4<\/p>\n\n\n\n

\n\n\n\n

8. In a year, Seema earns \u20b9 1,50,000 and saves \u20b9 50,000. Find the ratio of<\/span><\/strong><\/p>\n\n\n\n

(a) Money that Seema earns to the money she saves<\/strong><\/p>\n\n\n\n

Money earned by Seema = <\/strong>\u20b9 150000<\/p>\n\n\n\n

Money saved by her = \u20b9 50000<\/p>\n\n\n\n

Money spent by her = \u20b9 150000 \u2013 \u20b9 50000 = \u20b9 100000<\/p>\n\n\n\n

(a) Ratio of money earned to money saved = 150000 \/ 50000 = 15 \/ 5<\/p>\n\n\n\n

= 3 \/ 1<\/p>\n\n\n\n

\n\n\n\n

(b) Money that she saves to the money she spends.<\/strong><\/p>\n\n\n\n

Ratio of money saved to money spent = 50000 \/ 100000 = 5 \/ 10<\/p>\n\n\n\n

= 1 \/ 2<\/p>\n\n\n\n

\n\n\n\n

9. There are 102 teachers in a school of 3300 students. Find the ratio of the number of teachers to the number of students.<\/span><\/strong><\/p>\n\n\n\n

Solutions:<\/strong><\/p>\n\n\n\n

Given<\/p>\n\n\n\n

Number of teachers in a school = 102<\/p>\n\n\n\n

Number of students in a school = 3300<\/p>\n\n\n\n

Ratio of number of teachers to the number of students = 102 \/ 3300<\/p>\n\n\n\n

= (2 \u00d7 3 \u00d7 17) \/ (2 \u00d7 3 \u00d7 550)<\/p>\n\n\n\n

= 17 \/ 550<\/p>\n\n\n\n

\n\n\n\n

10. In a college, out of 4320 students, 2300 are girls. Find the ratio of<\/strong><\/p>\n\n\n\n

(a) Number of girls to the total number of students.<\/strong><\/p>\n\n\n\n

Given<\/p>\n\n\n\n

Total number of students = 4320<\/p>\n\n\n\n

Number of girls = 2300<\/p>\n\n\n\n

Number of boys = 4320 \u2013 2300<\/p>\n\n\n\n

= 2020<\/p>\n\n\n\n

\n\n\n\n

(a) Ratio of number of girls to the total number of students = 2300 \/ 4320<\/p>\n\n\n\n

= (2 \u00d7 2 \u00d7 5 \u00d7 115) \/ (2 \u00d7 2 \u00d7 5 \u00d7 216)<\/p>\n\n\n\n

= 115 \/ 216<\/p>\n\n\n\n

\n\n\n\n

(b) Number of boys to the number of girls.<\/strong><\/p>\n\n\n\n

Ratio of number of boys to the number of girls = 2020 \/ 2300<\/p>\n\n\n\n

= (2 \u00d7 2 \u00d7 5 \u00d7 101) \/ (2 \u00d7 2 \u00d7 5 \u00d7 115)<\/p>\n\n\n\n

= 101 \/ 115<\/p>\n\n\n\n

\n\n\n\n

(c) Number of boys to the total number of students.<\/strong><\/p>\n\n\n\n

Ratio of number of boys to the total number of students = 2020 \/ 4320<\/p>\n\n\n\n

= (2 \u00d7 2 \u00d7 5 \u00d7 101) \/ (2 \u00d7 2 \u00d7 5 \u00d7 216)<\/p>\n\n\n\n

= 101 \/ 216<\/p>\n\n\n\n

\n\n\n\n

11. Out of 1800 students in a school, 750 opted basketball, 800 opted cricket and remaining opted table tennis. If a student can opt only one game, find the ratio of<\/strong><\/p>\n\n\n\n

(a) Number of students who opted basketball to the number of students who opted table tennis.<\/strong><\/p>\n\n\n\n

Solutions:<\/strong><\/p>\n\n\n\n

(<\/strong>a) Ratio of number of students who opted basketball to the number of students who opted table tennis = 750 \/ 250 = 3 \/ 1<\/p>\n\n\n\n

(b) Number of students who opted cricket to the number of students opting basketball.<\/strong><\/p>\n\n\n\n

(b) Ratio of number of students who opted cricket to the number of students opting basketball = 800 \/ 750 = 16 \/ 15<\/p>\n\n\n\n

(c) Number of students who opted basketball to the total number of students.<\/strong><\/p>\n\n\n\n

(c) Ratio of number of students who opted basketball to the total number of students<\/p>\n\n\n\n

= 750 \/ 1800 = 25 \/ 60 = 5 \/ 12<\/p>\n\n\n\n

\n\n\n\n

12. Cost of a dozen pens is \u20b9 180 and cost of 8 ball pens is \u20b9 56. Find the ratio of the cost of a pen to the cost of a ball pen.<\/strong><\/p>\n\n\n\n

Solutions:<\/strong><\/p>\n\n\n\n

Cost of a dozen pens = <\/strong>\u20b9 180<\/p>\n\n\n\n

Cost of 1 pen = 180 \/ 12<\/p>\n\n\n\n

= \u20b9 15<\/p>\n\n\n\n

Cost of 8 ball pens = \u20b9 56<\/p>\n\n\n\n

Cost of 1 ball pen = 56 \/ 8<\/p>\n\n\n\n

= \u20b9 7<\/p>\n\n\n\n

Hence, required ratio is 15 \/ 7<\/p>\n\n\n\n

\n\n\n\n

13. Consider the statement: Ratio of breadth and length of a hall is 2: 5. Complete the following table that shows some possible breadths and lengths of the hall.<\/strong><\/p>\n\n\n\n

Solutions:<\/strong><\/p>\n\n\n\n

(i) <\/strong>Length = 50 m<\/p>\n\n\n\n

Breadth \/ 50 = 2 \/ 5<\/p>\n\n\n\n

By cross multiplication<\/p>\n\n\n\n

5\u00d7 breadth = 50 \u00d7 2<\/p>\n\n\n\n

Breadth = (50 \u00d7 2) \/ 5<\/p>\n\n\n\n

= 100 \/ 5<\/p>\n\n\n\n

= 20 m<\/p>\n\n\n\n

\n\n\n\n

(ii) Breadth = 40 m<\/p>\n\n\n\n

40 \/ Length = 2 \/ 5<\/p>\n\n\n\n

By cross multiplication<\/p>\n\n\n\n

2 \u00d7 Length = 40 \u00d7 5<\/p>\n\n\n\n

Length = (40 \u00d7 5) \/ 2<\/p>\n\n\n\n

Length = 200 \/ 2<\/p>\n\n\n\n

Length = 100 m<\/p>\n\n\n\n

\n\n\n\n

14. Divide 20 pens between Sheela and Sangeeta in the ratio of 3: 2.<\/strong><\/p>\n\n\n\n

Breadth of the hall (in metres)<\/strong><\/td>10<\/strong><\/td><\/td>40<\/strong><\/td><\/tr>
Length of the hall (in metres)<\/strong><\/td>25<\/strong><\/td> 50<\/strong><\/td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Solutions:<\/strong><\/p>\n\n\n\n

Terms of 3: 2 = 3 and 2<\/p>\n\n\n\n

Sum of these terms = 3 + 2<\/p>\n\n\n\n

= 5<\/p>\n\n\n\n

Now Sheela will get 3 \/ 5 of total pens and Sangeeta will get 2 \/ 5 of total pens<\/p>\n\n\n\n

Number of pens having with Sheela = 3 \/ 5 \u00d7 20<\/p>\n\n\n\n

= 3 \u00d7 4<\/p>\n\n\n\n

= 12<\/p>\n\n\n\n

Number of pens having with Sangeeta = 2 \/ 5 \u00d7 20<\/p>\n\n\n\n

= 2 \u00d7 4<\/p>\n\n\n\n

= 8<\/p>\n\n\n\n

\n\n\n\n

15. Mother wants to divide \u20b9 36 between her daughters Shreya and Bhoomika in the ratio of their ages. If age of Shreya is 15 years and age of Bhoomika is 12 years, find how much Shreya and Bhoomika will get.<\/strong><\/p>\n\n\n\n

Solutions:<\/strong><\/p>\n\n\n\n

Ratio of ages = 15 \/ 12<\/p>\n\n\n\n

= 5 \/ 4<\/p>\n\n\n\n

Hence, mother wants to divide \u20b9 36 in the ratio of 5: 4<\/p>\n\n\n\n

Terms of 5: 4 are 5 and 4<\/p>\n\n\n\n

Sum of these terms = 5 + 4<\/p>\n\n\n\n

= 9<\/p>\n\n\n\n

Here Shreya will get 5 \/ 9 of total money and Sangeeta will get 4 \/ 9 of total money<\/p>\n\n\n\n

The amount Shreya get = <\/strong>5 \/ 9 \u00d7 36<\/p>\n\n\n\n

= 20<\/p>\n\n\n\n

The amount Sangeeta get = 4 \/ 9 \u00d7 36<\/p>\n\n\n\n

= 16<\/p>\n\n\n\n

Therefore Shreya will get \u20b9 20 and Sangeeta will get \u20b9 16<\/p>\n\n\n\n

\n\n\n\n

16. Present age of father is 42 years and that of his son is 14 years. Find the ratio of<\/strong><\/p>\n\n\n\n

(a) Present age of father to the present age of son<\/strong><\/p>\n\n\n\n

(a) <\/strong>Present age of father = 42 years<\/p>\n\n\n\n

Present age of son = 14 years<\/p>\n\n\n\n

Required ratio 42 \/ 14<\/p>\n\n\n\n

= 3 \/ 1<\/p>\n\n\n\n

\n\n\n\n

(b) Age of the father to the age of son, when son was 12 years old.<\/strong><\/p>\n\n\n\n

The son was 12 years old 2 years ago. So the age of father 2 years ago will be<\/p>\n\n\n\n

= 42 \u2013 2 = 40 years<\/p>\n\n\n\n

Required ratio = 40 \/ 12 = (4 \u00d7 10) \/ (4 \u00d7 3) = 10 \/ 3<\/p>\n\n\n\n

\n\n\n\n

(c) Age of father after 10 years to the age of son after 10 years.<\/strong><\/p>\n\n\n\n

After ten years age of father = 42 + 10 = 52 years<\/p>\n\n\n\n

After 10 years age of son = 14 + 10 = 24 years<\/p>\n\n\n\n

Required ratio = 52 \/ 24 = (4 \u00d7 13) \/ (4 \u00d7 6)<\/p>\n\n\n\n

= 13 \/ 6<\/p>\n\n\n\n

\n\n\n\n

(d) Age of father to the age of son when father was 30 years old.<\/strong><\/p>\n\n\n\n

12 years ago, age of father was 30<\/p>\n\n\n\n

At that time age of son = 14 \u2013 12<\/p>\n\n\n\n

= 2 years<\/p>\n\n\n\n

Required ratio = 30 \/ 2 = (2 \u00d7 15) \/ 2<\/p>\n\n\n\n

= 15 \/ 1<\/p>\n\n\n\n

\n\n\n\n

Exercise 12.2<\/span><\/strong><\/p>\n\n\n\n

1. Determine if the following are in proportion.<\/span><\/strong><\/p>\n\n\n\n

(a) 15, 45, 40, 120<\/strong><\/p>\n\n\n\n

15, 45, 40, 120<\/p>\n\n\n\n

15 \/ 45 = 1 \/ 3<\/p>\n\n\n\n

40 \/ 120 = 1 \/ 3<\/p>\n\n\n\n

Hence, 15: 45 = 40:120<\/p>\n\n\n\n

\u2234 These are in a proportion<\/p>\n\n\n\n

\n\n\n\n

(b) 33, 121, 9, 96<\/strong><\/p>\n\n\n\n

33, 121, 9, 96<\/p>\n\n\n\n

33 \/ 121 = 3 \/ 11<\/p>\n\n\n\n

9 \/ 96 = 3 \/ 32<\/p>\n\n\n\n

Hence 33:121 \u2260 9: 96<\/p>\n\n\n\n

\u2234 These are not in a proportion<\/p>\n\n\n\n

\n\n\n\n

(c) 24, 28, 36, 48<\/strong><\/p>\n\n\n\n

24, 28, 36, 48<\/p>\n\n\n\n

24 \/ 28 = 6 \/ 7<\/p>\n\n\n\n

36 \/ 48 = 3 \/ 4<\/p>\n\n\n\n

Hence, 24: 28 \u2260 36:48<\/p>\n\n\n\n

\u2234 These are not in a proportion<\/p>\n\n\n\n

\n\n\n\n

(d) 32, 48, 70, 210<\/strong><\/p>\n\n\n\n

32, 48, 70, 210<\/p>\n\n\n\n

32 \/ 48 = 2 \/ 3<\/p>\n\n\n\n

70 \/ 210 = 1 \/ 3<\/p>\n\n\n\n

Hence, 32: 48 \u2260 70: 210<\/p>\n\n\n\n

\u2234 These are not in a proportion<\/p>\n\n\n\n

\n\n\n\n

(e) 4, 6, 8, 12<\/p>\n\n\n\n

4 \/ 6 = 2 \/ 3<\/p>\n\n\n\n

8 \/ 12 = 2 \/ 3<\/p>\n\n\n\n

Hence 4: 6 = 8: 12<\/p>\n\n\n\n

\u2234 These are in a proportion<\/p>\n\n\n\n

\n\n\n\n

(e) 4, 6, 8, 12<\/strong><\/p>\n\n\n\n

4, 6, 8, 12<\/p>\n\n\n\n

4 \/ 6 = 2 \/ 3<\/p>\n\n\n\n

8 \/ 12 = 2 \/ 3<\/p>\n\n\n\n

Hence 4: 6 = 8: 12<\/p>\n\n\n\n

\u2234 These are in a proportion<\/p>\n\n\n\n

\n\n\n\n

(f) 33, 44, 75, 100<\/strong><\/p>\n\n\n\n

33, 44, 75, 100<\/p>\n\n\n\n

33\/ 44 = 3\/ 4<\/p>\n\n\n\n

75 \/ 100 = 3 \/ 4<\/p>\n\n\n\n

Hence, 33:44 = 75: 100<\/p>\n\n\n\n

\u2234 These are in a proportion<\/p>\n\n\n\n

\n\n\n\n

2. Write True (T) or False ( F ) against each of the following statements :<\/strong><\/p>\n\n\n\n

(a) 16 : 24 :: 20 : 30<\/strong><\/p>\n\n\n\n

(a) <\/strong>16: 24 :: 20: 30<\/p>\n\n\n\n

16 \/ 24 = 2 \/ 3<\/p>\n\n\n\n

20 \/ 30 = 2 \/ 3<\/p>\n\n\n\n

Hence, 16: 24 = 20: 30<\/p>\n\n\n\n

Therefore True<\/p>\n\n\n\n

\n\n\n\n

(b) 21: 6 :: 35 : 10<\/strong><\/p>\n\n\n\n

21: 6:: 35: 10<\/p>\n\n\n\n

21 \/ 6 = 7 \/ 2<\/p>\n\n\n\n

35 \/ 10 = 7 \/ 2<\/p>\n\n\n\n

Hence, 21: 6 = 35: 10<\/p>\n\n\n\n

Therefore True<\/p>\n\n\n\n

\n\n\n\n

(c) 12 : 18 :: 28 : 12<\/strong><\/p>\n\n\n\n

12 \/ 18 = 2 \/ 3<\/p>\n\n\n\n

28 \/ 12 = 7 \/ 3<\/p>\n\n\n\n

Hence, 12: 18 \u2260 28:12<\/p>\n\n\n\n

Therefore False<\/p>\n\n\n\n

\n\n\n\n

(d) 8 : 9 :: 24 : 27<\/strong><\/p>\n\n\n\n

8: 9:: 24: 27<\/p>\n\n\n\n

We know that = 24 \/ 27 = (3 \u00d7 8) \/ (3 \u00d7 9)<\/p>\n\n\n\n

= 8 \/ 9<\/p>\n\n\n\n

Hence, 8: 9 = 24: 27<\/p>\n\n\n\n

Therefore True<\/p>\n\n\n\n

\n\n\n\n

(e) 5.2 : 3.9 :: 3 : 4<\/strong><\/p>\n\n\n\n

5.2: 3.9:: 3: 4<\/p>\n\n\n\n

As 5.2 \/ 3.9 = 3 \/ 4<\/p>\n\n\n\n

Hence, 5.2: 3.9 \u2260 3: 4<\/p>\n\n\n\n

Therefore False<\/p>\n\n\n\n

\n\n\n\n

(f) 0.9 : 0.36 :: 10 : 4<\/strong><\/p>\n\n\n\n

0.9: 0.36:: 10: 4<\/p>\n\n\n\n

0.9 \/ 0.36 = 90 \/ 36<\/p>\n\n\n\n

= 10 \/ 4<\/p>\n\n\n\n

Hence, 0.9: 0.36 = 10: 4<\/p>\n\n\n\n

Therefore True<\/p>\n\n\n\n

\n\n\n\n

3. Are the following statements true?<\/strong><\/p>\n\n\n\n

(a) 40 persons : 200 persons = \u20b9 15 : \u20b9 75<\/strong><\/p>\n\n\n\n

40 persons : 200 persons = \u20b9 15 : \u20b9 75<\/p>\n\n\n\n

40 \/ 200 = 1 \/ 5<\/p>\n\n\n\n

15 \/ 75 = 1 \/ 5<\/p>\n\n\n\n

Hence, True<\/p>\n\n\n\n

\n\n\n\n

(b) 7.5 litres : 15 litres = 5 kg : 10 kg<\/strong><\/p>\n\n\n\n

7.5 litres : 15 litres = 5 kg : 10 kg<\/p>\n\n\n\n

7.5 \/ 15 = 1 \/ 2<\/p>\n\n\n\n

5 \/ 10 = 1 \/ 2<\/p>\n\n\n\n

Hence, True<\/p>\n\n\n\n

\n\n\n\n

(c) 99 kg : 45 kg = \u20b9 44 : \u20b9 20<\/strong><\/p>\n\n\n\n

99 kg : 45 kg = \u20b9 44 : \u20b9 20<\/p>\n\n\n\n

99 \/ 45 = 11 \/ 5<\/p>\n\n\n\n

44 \/ 20 = 11 \/ 5<\/p>\n\n\n\n

Hence, True<\/p>\n\n\n\n

\n\n\n\n

(d) 32 m : 64 m = 6 sec : 12 sec<\/strong><\/p>\n\n\n\n

32 m : 64 m = 6 sec : 12 sec<\/p>\n\n\n\n

32 \/ 64 = 1 \/ 2<\/p>\n\n\n\n

6 \/ 12 = 1 \/ 2<\/p>\n\n\n\n

Hence, True<\/p>\n\n\n\n

\n\n\n\n

(e) 45 km : 60 km = 12 hours : 15 hours<\/strong><\/p>\n\n\n\n

45 km : 60 km = 12 hours : 15 hours<\/p>\n\n\n\n

45 \/ 60 = 3 \/ 4<\/p>\n\n\n\n

12 \/ 15 = 4 \/ 5<\/p>\n\n\n\n

Hence, False<\/p>\n\n\n\n

\n\n\n\n

4. Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.<\/strong><\/p>\n\n\n\n

(a) 25 cm : 1 m and \u20b9 40 : \u20b9 160<\/strong><\/p>\n\n\n\n

25 cm : 1 m and \u20b9 40 : \u20b9 160<\/p>\n\n\n\n

25 cm = 25 \/ 100 m<\/p>\n\n\n\n

= 0.25 m<\/p>\n\n\n\n

0.25 \/ 1 = 1 \/ 4<\/p>\n\n\n\n

40 \/ 160 = 1 \/ 4<\/p>\n\n\n\n

Yes, these are in a proportion<\/p>\n\n\n\n

Middle terms are 1 m, \u20b9 40 and Extreme terms are 25 cm, \u20b9 160<\/p>\n\n\n\n

\n\n\n\n

(b)39 litres : 65 litres and 6 bottles : 10 bottles<\/strong><\/p>\n\n\n\n

39 litres : 65 litres and 6 bottles : 10 bottles<\/p>\n\n\n\n

39 \/ 65 = 3 \/5<\/p>\n\n\n\n

Yes, these are in a proportion<\/p>\n\n\n\n

Middle terms are 65 litres, 6 bottles and Extreme terms are 39 litres, 10 bottles<\/p>\n\n\n\n

6 \/ 10 = 3 \/ 5<\/p>\n\n\n\n

\n\n\n\n

(c) 2 kg : 80 kg and 25 g : 625 g<\/strong><\/p>\n\n\n\n

2 kg : 80 kg and 25 g : 625 g<\/p>\n\n\n\n

2 \/ 80 = 1 \/ 40<\/p>\n\n\n\n

25 \/ 625 = 1 \/ 25<\/p>\n\n\n\n

No, these are not in a proportion<\/p>\n\n\n\n

\n\n\n\n

(d) 200 mL : 2.5 litre and \u20b9 4 : \u20b9 50<\/strong><\/p>\n\n\n\n

200 mL : 2.5 litre and \u20b9 4 : \u20b9 50<\/p>\n\n\n\n

1 litre = 1000 ml<\/p>\n\n\n\n

2.5 litre = 2500 ml<\/p>\n\n\n\n

200 \/ 2500 = 2 \/ 5<\/p>\n\n\n\n

4 \/ 50 = 2 \/ 25<\/p>\n\n\n\n

Yes, these are in a proportion<\/p>\n\n\n\n

Middle terms are 2.5 litres, \u20b9 4 and Extreme terms are 200 ml, \u20b9 50<\/p>\n\n\n\n

\n\n\n\n

Exercise 12.3<\/p>\n\n\n\n

1. If the cost of 7 m of cloth is \u20b9 1470, find the cost of 5 m of cloth.<\/strong><\/p>\n\n\n\n

Given<\/p>\n\n\n\n

Cost of 7 m cloth = \u20b9 1470<\/p>\n\n\n\n

Cost of 1 m cloth = 1470 \/ 7<\/p>\n\n\n\n

So, cost of 5 cloth = 210 \u00d7 5 = 1050<\/p>\n\n\n\n

\u2234 Cost of 5 m cloth is \u20b9 1050<\/p>\n\n\n\n

= \u20b9 210<\/p>\n\n\n\n

\n\n\n\n

Money earned by Ekta in 10 days = \u20b9 3000<\/p>\n\n\n\n

2. Ekta earns \u20b9 3000 in 10 days. How much will she earn in 30 days?<\/strong><\/p>\n\n\n\n

Money earned in one day by her = 3000 \/ 10<\/p>\n\n\n\n

= \u20b9 300<\/p>\n\n\n\n

So, money earned by her in 30 days = 300 \u00d7 30<\/p>\n\n\n\n

= \u20b9 9000<\/p>\n\n\n\n

\n\n\n\n

3. If it has rained 276 mm in the last 3 days, how many cm of rain will fall in one full week (7 days)? Assume that the rain continues to fall at the same rate.<\/strong><\/p>\n\n\n\n

Measure of rain in 3 days = 276 mm<\/p>\n\n\n\n

Measure of rain in one day = 276 \/ 3<\/p>\n\n\n\n

= 92 mm<\/p>\n\n\n\n

So, measure of rain in one week i.e 7 days = 92 \u00d7 7<\/p>\n\n\n\n

= 644 mm<\/p>\n\n\n\n

= 644 \/ 10<\/p>\n\n\n\n

= 64.4 cm<\/p>\n\n\n\n

\n\n\n\n

4. Cost of 5 kg of wheat is \u20b9 91.50.<\/strong><\/p>\n\n\n\n

(a) What will be the cost of 8 kg of wheat?<\/strong><\/p>\n\n\n\n

(b) What quantity of wheat can be purchased in \u20b9 183?<\/strong><\/p>\n\n\n\n

(a) <\/strong>Cost of 5 kg wheat = \u20b9 91.50.<\/p>\n\n\n\n

Cost of 1 kg wheat = 91.50 \/ 5<\/p>\n\n\n\n

= \u20b9 18.3<\/p>\n\n\n\n

So, cost of 8 kg wheat = 18.3 \u00d7 8<\/p>\n\n\n\n

= \u20b9 146.40<\/p>\n\n\n\n

(b) Wheat purchased in \u20b9 91.50 = 5 kg<\/p>\n\n\n\n

Wheat purchased in \u20b9 1 = 5 \/ 91.50 kg<\/p>\n\n\n\n

So, wheat purchased in \u20b9 183 = (5 \/ 91.50) \u00d7 183<\/p>\n\n\n\n

= 10 kg<\/p>\n\n\n\n

\n\n\n\n

5. The temperature dropped 15 degree celsius in the last 30 days. If the rate of temperature drop remains the same, how many degrees will the temperature drop in the next ten days?<\/strong><\/p>\n\n\n\n

Temperature drop in 30 days = 150<\/sup> C<\/p>\n\n\n\n

Temperature drop in 1 day = 15 \/ 30<\/p>\n\n\n\n

= (1 \/ 2)0<\/sup> C<\/p>\n\n\n\n

So, temperature drop in next 10 days = (1 \/ 2) \u00d7 10<\/p>\n\n\n\n

= 50<\/sup> C<\/p>\n\n\n\n

\u2234 The temperature drop in the next 10 days will be 50<\/sup> C<\/p>\n\n\n\n

\n\n\n\n

6. Shaina pays \u20b9 15000 as rent for 3 months. How much does she has to pay for a whole year, if the rent per month remains same?<\/strong><\/p>\n\n\n\n

Rent paid by Shaina in 3 months = \u20b9 15000<\/p>\n\n\n\n

Rent for 1 month = 15000 \/ 3<\/p>\n\n\n\n

= <\/strong>\u20b9 5000<\/p>\n\n\n\n

So, rent for 12 months i.e 1 year = 5000 \u00d7 12<\/p>\n\n\n\n

= <\/strong>\u20b9 60,000<\/p>\n\n\n\n

\u2234 Rent paid by Shaina in 1 year is \u20b9 60,000<\/p>\n\n\n\n

\n\n\n\n

7. Cost of 4 dozen bananas is \u20b9 180. How many bananas can be purchased for \u20b9 90?<\/strong><\/p>\n\n\n\n

Number of bananas bought in\u20b9 180 = 4 dozens<\/p>\n\n\n\n

= 4 \u00d7 12<\/p>\n\n\n\n

= 48 bananas<\/p>\n\n\n\n

Number of bananas bought in \u20b9 1 = 48 \/ 180<\/p>\n\n\n\n

So, number of bananas bought in \u20b9 90 = (48 \/ 180) \u00d7<\/strong> 90<\/p>\n\n\n\n

= 24 bananas<\/p>\n\n\n\n

\u2234 24 bananas can be purchased in \u20b9 90<\/p>\n\n\n\n

\n\n\n\n

8. The weight of 72 books is 9 kg. What is the weight of 40 such books?<\/strong><\/p>\n\n\n\n

Weight of 72 books = 9 kg<\/p>\n\n\n\n

Weight of 1 book = 9 \/ 72<\/p>\n\n\n\n

= 1 \/ 8 kg<\/p>\n\n\n\n

So, weight of 40 books = (1 \/ 8) \u00d7 40<\/p>\n\n\n\n

= 5 kg<\/p>\n\n\n\n

\u2234 Weight of 40 books is 5 kg<\/p>\n\n\n\n

\n\n\n\n

9. A truck requires 108 litres of diesel for covering a distance of 594 km. How much diesel will be required by the truck to cover a distance of 1650 km?<\/strong><\/p>\n\n\n\n

Diesel required for 594 km = 108 litres<\/p>\n\n\n\n

Diesel required for 1 km = 108 \/ 594<\/p>\n\n\n\n

= 2 \/ 11 litre<\/p>\n\n\n\n

So, diesel required for 1650 km = (2 \/ 11) \u00d7 1650<\/p>\n\n\n\n

= 300 litres<\/p>\n\n\n\n

\u2234 Diesel required by the truck to cover a distance of 1650 km is 300 litres<\/p>\n\n\n\n

\n\n\n\n

10. Raju purchases 10 pens for \u20b9 150 and Manish buys 7 pens for \u20b9 84. Can you say who got the pens cheaper?<\/strong><\/p>\n\n\n\n

Pens purchased by Raju in \u20b9 150 = 10 pens<\/p>\n\n\n\n

Cost of 1 pen = 150 \/ 10<\/p>\n\n\n\n

= \u20b9 15<\/p>\n\n\n\n

Pens purchased by Manish in \u20b9 84 = 7 pens<\/p>\n\n\n\n

Cost of 1 pen = 84 \/ 7<\/p>\n\n\n\n

= \u20b9 12<\/p>\n\n\n\n

\u2234 Pens purchased by Manish are cheaper than Raju<\/p>\n\n\n\n

\n\n\n\n

11. Anish made 42 runs in 6 overs and Anup made 63 runs in 7 overs. Who made more runs per over?<\/strong><\/p>\n\n\n\n

Runs made by Anish in 6 overs = 42<\/p>\n\n\n\n

Runs made by Anish in 1 over = 42 \/ 6<\/p>\n\n\n\n

= 7<\/p>\n\n\n\n

Runs made by Anup in 7 overs = 63<\/p>\n\n\n\n

Runs made by Anup in 1 over = 63 \/ 7<\/p>\n\n\n\n

= 9<\/p>\n\n\n\n

\u2234 Anup scored more runs than Anish.<\/p>\n","protected":false},"excerpt":{"rendered":"

Summary of ratio and proportion Solved exercise of ration and proportion Summary Ratio: We compare two quantities. This comparison is known as the ratio. Ratio is denoted by symbol : Example: The ratio of...<\/p>\n","protected":false},"author":3,"featured_media":2154,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[115,475,14],"tags":[257,258,259],"cp_meta_data":{"_edit_lock":["1629956048:2"],"_last_editor_used_jetpack":["block-editor"],"_thumbnail_id":["2154"],"_jetpack_related_posts_cache":["a:1:{s:32:\"8f6677c9d6b0f903e98ad32ec61f8deb\";a:2:{s:7:\"expires\";i:1776444407;s:7:\"payload\";a:3:{i:0;a:1:{s:2:\"id\";i:1991;}i:1;a:1:{s:2:\"id\";i:3538;}i:2;a:1:{s:2:\"id\";i:2711;}}}}"],"_edit_last":["2"]},"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/themindpalace.in\/wp-content\/uploads\/2020\/12\/Slide1-4.jpg","jetpack-related-posts":[],"_links":{"self":[{"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/posts\/2152"}],"collection":[{"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/comments?post=2152"}],"version-history":[{"count":7,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/posts\/2152\/revisions"}],"predecessor-version":[{"id":2498,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/posts\/2152\/revisions\/2498"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/media\/2154"}],"wp:attachment":[{"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/media?parent=2152"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/categories?post=2152"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/themindpalace.in\/index.php\/wp-json\/wp\/v2\/tags?post=2152"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}