- Two quantities can be compared only if they are in the same unit.
- For comparing quantities of the same type, we commonly use the method of taking difference between the quantities.
- Sometimes the comparison is made by using division.
- For comparison by ratio, the two quantities must be in the same ratio.
- We can get equivalent ratios by multiplying or dividing the numerator and denominator by the same number.
- If two ratios are equal, we say that they are in proportion and use the symbol ‘::’ or ‘=’ to equate the two ratios.
- If two ratios are not equal, then we say that they are not in proportion. In a statement of proportion, the four quantities involved when taken in order are known as respective terms. First and fourth terms are known as extreme terms. Second and third terms are known as middle terms.
- The method in which first we find the value of one unit and then the value of required number of units is known as Unitary Method.
Page No 251:
Question 1:
There are 20 girls and 15 boys in a class.
(a) What is the ratio of number of girls to the number of boys?
(b)What is the ratio of number of girls to the total number of students in the class?
Answer:
Number of girls = 20
Number of boys = 15
Total number of students = 20 + 15 = 35
(a) Ratio
of number of girls to boys =
(b) Ratio
of number of girls to total students =
Page No 251:
Question 2:
Out of 30 students in a class, 6 like football, 12 like cricket and remaining like tennis. Find the ratio of
(a) Number of students liking football to number of students liking tennis.
(b) Number of students liking cricket to total number of students.
Answer:
Number of students who like football = 6
Number of students who like cricket = 12
Number of students who like tennis = 30 − 6 − 12 = 12
(a) Ratio of the number of students liking football to the number of students liking tennis =
(b) Ratio of the number of students liking cricket to the total number of
students =
Video Solution for ratio and proportion (Page: 251 , Q.No.: 2)
NCERT Solution for Class 6 math - ratio and proportion 251 , Question 2
Page No 251:
Question 3:
See the figure and find the ratio of
(a) Number of triangles to the number of circles inside the rectangle.
(b) Number of squares to all the figures inside the rectangle.
(c) Number of circles to all the figures inside the rectangle.
Answer:
Number of triangles = 3
Number of circles = 2
Number of squares = 2
Total number of figures = 7
(a) Ratio of the number of triangles to the number of circles =
(b) Ratio of the number of squares to all the figures in the rectangle =
(c) Ratio of the number of circles to all the figures in the rectangle =
Video Solution for ratio and proportion (Page: 251 , Q.No.: 3)
NCERT Solution for Class 6 math - ratio and proportion 251 , Question 3
Page No 251:
Question 4:
Distances 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.
Answer:
The distance travelled in an hour by a certain object is called the speed of that object.
Distance travelled by Hamid in one hour = 9 km
Distance travelled by Akhtar in one hour = 12 km
Hamid’s speed = 9 km/hr
Akhtar’s speed = 12 km/hr
Page No 251:
Question 5:
Fill in the following blanks:
[Are
these equivalent ratios?]
Answer:
Therefore, 5, 12, 25 will come in the blanks respectively.
Yes, all these are equivalent ratios.
Page No 251:
Question 6:
Find the ratio of the following:
(a) 81 to 108 (b) 98 to 63
(c) 33 km to 121 km (d) 30 minutes to 45 minutes
Answer:
(a)
(b)
(c)
(d)
Page No 251:
Question 7:
Find the ratio of the following:
(a) 30 minutes to 1.5 hours (b) 40 cm to 1.5 m
(c) 55 paise to Re1 (d) 500 mL to 2 litres
Answer:
(a) 30 min
=
Required ratio =
(b) 40 cm to 1.5 m
1.5 m = 150 cm
Required ratio =
(c) 55 paise to Re 1
Re 1 = 100 paise
Required ratio =
(d) 500 mL to 2l
1l = 1000 mL
2l = 2000 mL
Required ratio =
Page No 251:
Question 8:
In a year, Seema earns Rs 1, 50, 000 and saves Rs 50, 000. Find the ratio of
(a) Money that Seema earns to the money she saves.
(b) Money that she saves to the money she spends.
Answer:
Money earned = Rs 150000
Money saved = Rs 50000
Money spent = Rs 150000 − Rs 50000 = Rs 100000
(a) Ratio
of money earned to money saved =
(b) Ratio
of money saved to money spent =
Page No 251:
Question 9:
There are 102 teachers in a school of 3300 students. Find the ratio of the number of teachers to the number of students.
Answer:
Ratio
required =
Page No 251:
Question 10:
In a college, out of 4320 students, 2300 are girls. Find the ratio of
(a) Number of girls to the total number of students.
(b) Number of boys to the number of girls.
(c) Number of boys to the total number of students.
Answer:
Total number of students = 4320
Number of girls = 2300
Number of boys = 4320 − 2300 = 2020
(a) Required
ratio =
(b) Required
ratio =
(c) Required
ratio =
Page No 252:
Question 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
(a) Number of students who opted basketball to the number of students who opted table tennis.
(b) Number of students who opted cricket to the number of students opting basketball.
(c) Number of students who opted basketball to the total number of students.
Answer:
(a) Required
ratio =
(b) Required
ratio =
(c) Required
ratio =
Page No 252:
Question 12:
Cost of a dozen pens is Rs 180 and cost of 8 ball pens is Rs 56. Find the ratio of the cost of a pen to the cost of a ball pen.
Answer:
Cost of a dozen pens = Rs 180
Cost of 1
pen =
Cost of 8 ball pens = Rs 56
Cost of a
ball pen =
Required
ratio =
Page No 252:
Question 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.
|
Breadth of the hall (in metres) |
10 |
? |
40 |
|
Length of the hall (in metres) |
25 |
50 |
? |
Answer:
(i) Length = 50 m
5 × Breadth = 50 × 2 (By cross-multiplication)
Breadth = 20 m
(ii) Breadth = 40 m
2 × Length = 5 × 40 (By cross-multiplication)
Length = 100 m
Page No 252:
Question 14:
Divide 20 pens between Sheela and Sangeeta in the ratio of 3:2.
Answer:
Terms of 3 : 2 are 3 and 2.
Sum of these terms = 3 + 2 = 5
Sheela will get of total pens and Sangeeta will get of total pens.
Number of pens with Sheela =
Number of pens with Sangeeta =
Video Solution for ratio and proportion (Page: 252 , Q.No.: 14)
NCERT Solution for Class 6 math - ratio and proportion 252 , Question 14
Page No 252:
Question 15:
Mother wants to divide Rs 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.
Answer:
Ratio of ages =
Therefore, mother wants to divide Rs 36 in a ratio of 5 : 4.
Terms of 5 : 4 are 5 and 4.
Sum of these terms = 5 + 4 = 9
Shreya will get of the total money and Bhoomika will get of it.
Amount that Shreya will get =
Amount that Bhoomika will get =
Therefore, Shreya and Bhoomika will get Rs 20 and Rs 16 respectively.
Video Solution for ratio and proportion (Page: 252 , Q.No.: 15)
NCERT Solution for Class 6 math - ratio and proportion 252 , Question 15
Page No 252:
Question 16:
Present age of father is 42 years and that of his son is 14 years. Find the ratio of
(a) Present age of father to the present age of son.
(b) Age of the father to the age of son, when son was 12 years old.
(c) Age of father after 10 years to the age of son after 10 years.
(d) Age of father to the age of son when father was 30 years old.
Answer:
(a) Present age of father = 42 years
Present age of son = 14 years
Required ratio =
(b) Two years ago, the age of the son was 12 years and the age of the father was 42 − 2 = 40 years
Required ratio =
(c) After 10 years, the age of the father and son will be 52 years and 24 years respectively.
Required ratio =
(d) 12 years ago, the father was 30 years old.
At that time, age of son = 14 − 12 = 2 years
Required ratio =
Page No 255:
Question 1:
Determine if the following are in proportion.
(a) 15, 45, 40, 120 (b) 33, 121, 9, 96
(c) 24, 28, 36, 48 (d) 32, 48, 70, 210
(e) 4, 6, 8, 12 (f) 33, 44, 75, 100
Answer:
(a) 15, 45, 40, 120
Therefore, 15: 45 = 40: 120
Hence, these are in proportion.
(b) 33, 121, 9, 96
Therefore, 33: 121 ≠ 9: 96
Hence, these are not in proportion.
(c) 24, 28, 36, 48
Therefore, 24: 28 ≠ 36: 48
Hence, these are not in proportion.
(d) 32, 48, 70, 210
Therefore, 32: 48 ≠ 70: 210
Hence, these are not in proportion.
(e) 4, 6, 8, 12
Therefore, 4: 6 = 8: 12
Hence, these are in proportion.
(f) 33, 44, 75, 100
Therefore, 33: 44 = 75: 100
Hence, these are in proportion.
Page No 255:
Question 2:
Write True (T) or False (F) against each of the following statements:
(a) 16:24::20:30 (b) 21:6::35:10
(c) 12:18::28:12 (d) 8:9::24:27
(e) 5.2:3.9::3:4 (f) 0.9:0.36::10:4
Answer:
(a) 16: 24:: 20: 30
Therefore, 16: 24 = 20: 30
Hence, True
(b) 21: 6:: 35: 10
Therefore, 21: 6 = 35: 10
Hence, True
(c) 12: 18:: 28: 12
Therefore, 12: 18 ≠ 28: 12
Hence, False
(d) 8: 9:: 24: 27
As,
Therefore, True
(e) 5.2: 3.9:: 3: 4
As
,
Therefore, 5.2: 3.9 ≠ 3: 4
Hence, False
(f) 0.9: 0.36:: 10: 4
Therefore, 0.9: 0.36 = 10: 4
Hence, True
Page No 256:
Question 3:
Are the following statements true?
(a) 40 persons: 200 persons = Rs 15: Rs 75
(b) 7.5 litres: 15 litres = 5 kg: 10 kg
(c) 99 kg: 45 kg = Rs 44: Rs 20
(d) 32 m: 64 m = 6 sec: 12 sec
(e) 45 km: 60 km = 12 hours: 15 hours
Answer:
(a) 40 persons: 200 persons = Rs 15: Rs 75
True
(b) 7.5 l: 15 l = 5 kg: 10 kg
True
(c) 99 kg: 45 kg = Rs 44: Rs 20
True
(d) 32 m: 64 m = 6 sec: 12 sec
True
(e) 45 km: 60 km = 12 hrs: 15 hrs
False
Page No 256:
Question 4:
Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
(a) 25 cm: 1 m and Rs 40 : Rs 160
(b) 39 litres: 65 litres and 6 bottles: 10 bottles
(c) 2 kg: 80 kg and 25 g: 625 g
(d) 200 mL: 2.5 litre and Rs 4: Rs 50
Answer:
(a) 25cm: 1 m and Rs 40: Rs 160
25 cm ==
0.25 m
Yes. These are in proportion.
Middle terms are 1m, Rs 40.
Extreme terms are 25 cm, Rs 160.
(b) 39 l: 65 l and 6 bottles: 10 bottles
Yes. These are in proportion.
Middle terms are 65 l, 6 bottles.
Extreme terms are 39 l, 10 bottles.
(c) 2 kg: 80 kg and 25g: 625 g
No. These are not in proportion.
(d) 200 mL: 2.5 l and Rs 4: Rs 50
1 l = 1000 mL
2.5 l = 2500 mL
Yes. These are in proportion.
Middle terms are 2.5 l, Rs 4.
Extreme terms are 200 mL, Rs 50.
Page No 259:
Question 1:
If the cost of 7 m of cloth is Rs 1470, find the cost of 5 m of cloth.
Answer:
Cost of 7 m cloth = Rs 1470
Cost of 1 m cloth =
Therefore, cost of 5 m cloth = 210 × 5 = Rs 1050
Page No 259:
Question 2:
Ekta earns Rs 3000 in 10 days. How much will she earn in 30 days?
Answer:
Money earned in 10 days = Rs 3000
Money earned in 1 day = = Rs 300
Therefore, money earned in 30 days = 300 × 30 = Rs 9000
Page No 259:
Question 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.
Answer:
Measure of rain in 3 days = 276 mm
Measure of rain in 1 day =
Therefore, measure of rain in 7 days = 92 × 7 = 644 mm
Video Solution for ratio and proportion (Page: 259 , Q.No.: 3)
NCERT Solution for Class 6 math - ratio and proportion 259 , Question 3
Page No 259:
Question 4:
Cost of 5 kg of wheat is Rs 91.50.
(a) What will be the cost of 8 kg of wheat?
(b) What quantity of wheat can be purchased in Rs 183?
Answer:
(a) Cost of 5 kg wheat = Rs 91.50
Cost of 1 kg wheat =
Therefore, cost of 8 kg wheat = 18.30 × 8 = Rs 146.40
(b) Wheat purchased in Rs 91.50 = 5 kg
Wheat purchased in Re 1 = kg
Therefore, wheat purchased in Rs 183 = = 10 kg
Page No 259:
Question 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?
Answer:
Temperature drop in 30 days = 15°C
Temperature
drop in 1 day =
Therefore,
temperature drop in next 10 days =
Thus, there will be a temperature drop of 5ºC in the next ten days.
Page No 259:
Question 6:
Shaina pays Rs 15000 as rent for 3 months. How much does she has to pay for a whole year, if the rent per month remains same?
Answer:
Rent for 3 months = Rs 15000
Rent for 1 month = = Rs 5000
Therefore, rent for 12 months = 5000 × 12 = 60000
Thus, she has to pay Rs 60000 for a whole year.
Page No 259:
Question 7:
Cost of 4 dozens bananas is Rs 180. How many bananas can be purchased for Rs 90?
Answer:
Numbers of bananas bought in Rs 180 = 4 dozens = 4 × 12 = 48
Number of bananas bought in Re 1 =
Therefore, number of bananas bought in Rs 90 = = 24 bananas
Thus, 24 bananas can be purchased for Rs 90.
Video Solution for ratio and proportion (Page: 259 , Q.No.: 7)
NCERT Solution for Class 6 math - ratio and proportion 259 , Question 7
Page No 259:
Question 8:
The weight of 72 books is 9 kg. What is the weight of 40 such books?
Answer:
Weight of 72 books = 9 kg
Weight of
1 book =
Therefore,
weight of 40 books =
Thus, the weight of 40 such books is 5 kg.
Page No 259:
Question 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?
Answer:
Diesel required for 594 km = 108 litres
Diesel required for 1 km = =
Therefore, diesel required for 1650 km = = 300 litres
Thus, 300 litres diesel will be required by the truck to cover a distance of 1650 km.
Video Solution for ratio and proportion (Page: 259 , Q.No.: 9)
NCERT Solution for Class 6 math - ratio and proportion 259 , Question 9
Page No 259:
Question 10:
Raju purchases 10 pens for Rs 150 and Manish buys 7 pens for Rs 84. Can you say who got the pens cheaper?
Answer:
Raju purchased 10 pens for Rs 150.
∴
Price of 1 pen =
Manish purchased 7 pens for Rs 84.
∴
Price of 1 pen =
Therefore, Manish got the pens cheaper.
Page No 259:
Question 11:
Anish made 42 runs in 6 overs and Anup made 63 runs in 7 overs. Who made more runs per over?
Answer:
Runs made by Anish in 6 overs = 42
∴
Runs made by Anish in 1 over =
Runs made by Anup in 7 overs = 63
∴
Runs made by Anup in 1 over =
=
9
Clearly, Anup made more runs per over.
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