NCERT Exemplar Class 6 Maths Ratio and Proportion Solution: NCERT Exemplar Solution Class 6 Maths Chapter 8 Ratio and Proportion Full Explanation. NCERT Exemplar Class 6 Maths – Chapter 8 Ratio and Proportion. NCERT Exemplar Class 6 Maths Ratio and Proportion Solution by Expert.
NCERT Exemplar Class 6 Maths Ratio and Proportion Solution
In questions 1 to 10, only one of the four options is correct. Write the correct one.
Question 1:
The ratio of 8 books to 20 books is
(A) 2 : 5
(B) 5 : 2
(C) 4 : 5
(D) 5 : 4
Solution: Answer is A.
8/20 = (4 × 2)/(4 × 5) = 2/5
Question 2:
The ratio of the number of sides of a square to the number of edges
of a cube is
(A) 1 : 2
(B) 3 : 2
(C) 4 : 1
(D) 1 : 3
Solution: Answer is D.
(Number of side of square)/(Number of edges of cube) = 4/5 = 1/3
Question 3:
A picture is 60cm wide and 1.8m long. The ratio of its width to its perimeter in lowest form is
(A) 1 : 2
(B) 1 : 3
(C) 1 : 4
(D) 1 : 8
Solution: Answer is D.
60cm = 0.6m, Perimeter = l x b
= 0.6 x 1.8
= 1.08
Width/Perimeter = 0.6/1.08 = 1/8
Question 4:
Neelam’s annual income is Rs. 288000. Her annual savings amount to Rs. 36000. The ratio of her savings to her expenditure is
(A) 1 : 8
(B) 1 : 7
(C) 1 : 6
(D) 1 : 5
Solution: Answer is A.
Neelam annual income is 288000 and saving is 86000.
= 288000 – 36000
= 252000
Saving/expenditure = 36000/252000 = = 1/8
Question 5:
Mathematics textbook for Class VI has 320 pages. The chapter ‘symmetry’ runs from page 261 to page 272. The ratio of the number of pages of this chapter to the total number of pages of the book is
(A) 11 : 320
(B) 3 : 40
(C) 3 : 80
(D) 272 : 320
Solution: Answer is C.
(The number of pages of the chapter symmetry)/(Total number of pages of this book) = 12/320 = 3/80
Question 6:
In a box, the ratio of red marbles to blue marbles is 7:4. Which of the following could be the total number of marbles in the box?
(A) 18
(B) 19
(C) 21
(D) 22
Solution: Answer is D.
7/4 = (Red marbles)/(blue marbles) = 7 + 4 = 11 and 22 is the multiple of 11.
Question 7:
On a shelf, books with green cover and that with brown cover are in the ratio 2:3. If there are 18 books with green cover, then the number of books with brown cover is
(A) 12
(B) 24
(C) 27
(D) 36
Solution: Answer is C.
(Green colours)/(brown colours) = 2/3 = 18/x
= 18 X 3 = 2 × x
54 = 2x
x = 54/2
x = 27
The number of books with brown covers 27.
Question 8:
The greatest ratio among the ratios 2 : 3, 5 : 8, 75 : 121 and 40 : 25 is
(A) 2 : 3
(B) 5 : 8
(C) 75 : 121
(D) 40 : 25
Solution: Answer is D.
From above the option in denominator greater than numerator and in option D) Numerator greater than denominator means values increase 40:25 is the greater ratio among all.
Question 9:
There are ‘b’ boys and ‘g’ girls in a class. The ratio of the number of boys to the total number of students in the class is:
(A) b/b+g
(B) g/b+g
(C) b/g
(D) b+g/b
Solution: Answer is A.
Boys/(Total number of students) = b/(b+g).
Question 10:
If a bus travels 160 km in 4 hours and a train travels 320km in 5 hours at uniform speeds, then the ratio of the distances travelled by them in one hour is
(A) 1 : 2
(B) 4 : 5
(C) 5 : 8
(D) 8 : 5
Solution: Answer is C.
Speed = (Distance)/Time
Travelled by bus = 160/4 = 40 km/Hr
Travelled by Train = 320/5 = 64 km/Hr
40/64 = (8 × 5)/(8 × 8) = 5/8
In questions 11 to 15, find the missing number in the box in each of the proportions:
Question 11:
3/5 = —/20
Solution: 3/5 = 12/20
Question 12:
—/18 = 2/9
Solution: 4/18 = 2/9
Question 13:
8/— = 3.2/4
Solution: 8/10 = 3.2/4
Question 14:
—/45 = 16/40 = 24/—
Solution: 18/45 = 16/40 = 24/60
Question 15:
16/36 = —/63 = 36/— = —/117
Solution: 16/36 = 28/63 = 36/81 = 52/117
In questions 16 to 34, state whether the given statements are true (T) or false (F)
Question 16:
3/8 = 15/40
Solution: The statement is True.
Question 17:
4 : 7 = 20 : 35
Solution: The statement is True.
Question 18:
0.2 : 5 = 2 : 0.5
Solution: False
0.2/5 = 2/0.5 is false, 0.2/5 = 2/50 is true.
Question 19:
3 : 33 = 33 : 333
Solution: False
3/33 = 1/11 is true.
Question 20:
15m : 40m = 35m : 65m
Solution: False
15m/40m = 3/8, 35m/65m = 7/13 so there ratio is not equal.
Question 21:
27cm² : 57cm² = 18cm : 38cm
Solution: The statement is True.
Question 22:
5kg : 7.5kg = Rs 7.50 : Rs 5
Solution: False
It is not possible we can’t replace numerator to denominator for making equal.
Question 23:
20g : 100g = 1metre : 500cm
Solution: The statement is True.
Question 24:
12 hours : 30 hours = 8km : 20km
Solution: The statement is True.
Question 25:
12 hours : 30 hours = 8km : 20km
Solution: The statement is True.
Question 26:
The ratio of 150cm to 1metre is 1:1.5.
Solution: False
150cm/1m = 1.5m/1m = 1.5/1 = is true.
Question 27:
25kg : 20g = 50kg : 40g
Solution: The statement is True.
Question 28:
The ratio of 1 hour to one day is 1:1.
Solution: False
(1 Hr)/(24 Hr) = 1/24 is true.
Question 29:
The ratio 4 :16 is in its lowest form.
Solution: False
4/16 = 1/4 is its lowest form.
Question 30:
The ratio 5 : 4 is different from the ratio 4 : 5.
Solution: The statement is True.
Question 31:
A ratio will always be more than 1.
Solution: False
The ratio may more than 1.
Question 32:
A ratio can be equal to 1.
Solution: The statement is True.
Question 33:
If b : a = c : d, then a, b, c, d are in proportion.
Solution: False
b/a = c/a then we can’t say that a, b, c, d is in proportion.
Question 34:
The two terms of a ratio can be in two different units.
Solution: False
The two term of a ratio cannot be in two different units.
In questions 35 to 46, fill in the blanks to make the statements true.
Question 35:
A ratio is a form of comparison by ______.
Solution: A ratio is a form of comparison by division.
Question 36:
20m: 70m = Rs 8: Rs _____.
Solution: 20m: 70m = Rs 8: Rs 28.
Question 37:
There is a number in the box such that, 24, 9, 12 are in proportion. The number in the box is _____.
Solution: There is a number in the box such that, 24, 9, 12 are in proportion. The number in the box is 18.
Question 38:
If two ratios are equal, then they are in _____. Use Fig. 8.2 (In which each square is of unit length) for questions 39 and 40:
Solution: If two ratios are equal, then they are in proportion. Use Fig. 8.2 (In which each square is of unit length) for questions 39 and 40:
Question 39:
The ratio of the perimeter of the boundary of the shaded portion to the perimeter of the whole figure is ______.
Solution: The ratio of the perimeter of the boundary of the shaded portion to the perimeter of the whole figure is 3 : 7.
Question 40:
The ratio of the area of the shaded portion to that of the whole figure is ______.
Solution: The ratio of the area of the shaded portion to that of the whole figure is 1 : 6.
Question 41:
Sleeping time of a python in a 24-hour clock is represented by the shaded portion in Fig. 8.3.
The ratio of sleeping time to awaking time is ______.
Solution: The ratio of sleeping time to awaking time is 3 : 1.
Question 42:
A ratio expressed in lowest form has no common factor other than ______ in its terms.
Solution: A ratio expressed in lowest form has no common factor other than
One in its terms.
Question 43:
To find the ratio of two quantities, they must be expressed in _____ units.
Solution: To find the ratio of two quantities, they must be expressed in Same units.
Question 44:
Ratio of 5 paise to 25 paise is the same as the ratio of 20 paise to _____.
Solution: Ratio of 5 paise to 25 paise is the same as the ratio of 20 paise to 100 paise.
Question 45:
Saturn and Jupiter take 9 hours 56 minutes and 10 hours 40 minutes, respectively for one spin on their axes. The ratio of the time taken by Saturn and Jupiter in lowest form is ______.
Solution: Saturn and Jupiter take 9 hours 56 minutes and 10 hours 40 minutes, respectively for one spin on their axes. The ratio of the time taken by Saturn and Jupiter in lowest form is 149: 160.
Question 46:
10g of caustic soda dissolved in 100mL of water makes a solution of caustic soda. Amount of caustic soda needed for 1 litre of water to make the same type of solution is ______.
Solution: 10g of caustic soda dissolved in 100mL of water makes a solution of caustic soda. Amount of caustic soda needed for 1 litre of water to make the same type of solution is 100gm.
Question 47:
The marked price of a table is Rs 625 and its sale price is Rs 500. What is the ratio of the sale price to the marked price?
Solution: (sale price)/(marked price) 500/625 = 20/25 = 4/5
Question 48:
Which pair of ratios are equal? And why?
(i) 2/3, 4/6
(ii) 8/4 , 2/1
(iii) 4/5, 12/20
Solution:
This ratio is equal because (2 x 2)/(3 x 2) = 4/6 numerator and denominator are multiplied by same number.
(ii) This pair of ratios are equal because (8 ÷ 4)/(4 ÷ 4) = 2/1 denominator is divided by same number.
(iii) This pair of ratios are not equal.
Question 49:
Which ratio is larger 10 : 21 or 21 : 93?
Solution:
10/21 = 0.476
21/93 = 0.225
10/21 is larger ratio.
Question 50:
Reshma prepared 18kg of Burfi by mixing Khoya with sugar in the ratio of 7 : 2. How much Khoya did she use?
Solution:
7x + 2x = 18
9x = 18
x = 18/9
x = 2
7 × 2 = 14 khoya she uses.
Question 51:
A line segment 56cm long is to be divided into two parts in the ratio
of 2 : 5. Find the length of each part.
Solution:
2x + 5x = 56
7x = 56
X = 56/7
X = 8
2x = 16, 5x = 40
16, 40 is the length of each part.
Question 52:
The number of milk teeth in human beings is 20 and the number of permanent teeth is 32. Find the ratio of the number of milk teeth to the number of permanent teeth.
Solution: (milk teeth)/(permanent teeth) = 20/32 = 5/8
Question 53:
Sex ratio is defined as the number of females per 1000 males in the population. Find the sex ratio if there are 3732 females per 4000 males in a town.
Solution:
number of males in a town is 4000
number of females in a town is 3732
female/male = 3732/4000
= 933/1000
As sex ratio is the number of females per 1000 males.
Question 54:
In a year, Ravi earns Rs 360000 and paid Rs 24000 as income tax. Find the ratio of his
(a) income to income tax.
(b) income tax to income after paying income tax.
Solution:
(a) 360000/24000 = 15/1
(b) 24000/336000 = 1/14
Question 55:
Ramesh earns Rs 28000 per month. His wife Rama earns Rs 36000 per month. Find the ratio of
(a) Ramesh’s earnings to their total earnings
(b) Rama’s earnings to their total earnings.
Solution:
(a) 28000/(36000+28000) = 28000/64000 = 7/16
(b) 36000/64000 = 9/16
Question 56:
Of the 288 persons working in a company, 112 are men and the remaining are women. Find the ratio of the number of
(a) men to that of women.
(b) men to the total number of persons.
(c) women to the total number of persons.
Solution:
(a) 112/288 = (7 men)/(18 total number of person)
(c) 176/288 = (11 women)/(18 total number of person)
Question 57:
A rectangular sheet of paper is of length 1.2m and width 21cm. Find the ratio of width of the paper to its length.
Solution: Width/Length = 0.21m/1.2m = 21/120
100cm = 1m
Question 58:
A scooter travels 120km in 3 hours and a train travels 120km in 2 hours.
Find the ratio of their speeds
(Hint: Speed = distance travelled/time taken)
Solution:
Scooter travels = 120/3 = 40km/Hr
Train travels = 120/2 = 60km/Hr
= 40/60 = 2/3 ratio of their speed
Question 59:
An office opens at 9 a.m. and closes at 5.30 p.m. with a lunch break of 30 minutes. What is the ratio of lunch break to the total period in the office?
Solution:
30 minute means half hour we denoted as 1/2
Question 60:
The shadow of a 3m long stick is 4m long. At the same time of the day, if the shadow of a flagstaff is 24m long, how tall is the flagstaff?
Solution:
3/4 = x/24
3 x 24 = 4 × X
X = (3 × 24)/4
X = 18 m
18m tall is flagstaff.
Question 61:
A recipe calls for 1 cup of milk for every 2 1/2 cups of flour to make a cake that would feed 6 persons. How many cups of both flour and milk will be needed to make a similar cake for 8 people?
Solution: (1 + 2 1/2 ) = 1 + 5/2 = 7/2 is the amount of both
Flour and milk to make the cake for 6 person
7/2 : 6 :: X : 8
X is the cup of flour and milk to make cake for 8 persons.
2/6 = x/8
6 × X = 8 × 7/2
X = 28/7
X = 14/3
Question 62:
In a school, the ratio of the number of large classrooms to small classrooms is 3:4. If the number of small rooms is 20, then find the number of large rooms.
Solution: (Large classroom)/(Small classroom) = 3/4 = X/20
20 x 3 = 4 x X
60 = 4X
X = 15 number of large classrooms
Question 63:
Samira sells newspapers at Janpath crossing daily. On a particular day, she had 312 newspapers out of which 216 are in English and remaining in Hindi. Find the ratio of
(a) the number of English newspapers to the number of Hindi newspapers.
(b) the number of Hindi newspapers to the total number of newspapers
Solution:
(a) (216 English)/(96 Hindi) = 9/4
(b) (96 Hindi)/(312 Newspaper) = 4/13
Question 64:
The students of a school belong to different religious backgrounds. The number of Hindu students is 288, the number of Muslim students is 252, the number of Sikh students is 144 and the number of Christian students is 72. Find the ratio of
(a) the number of Hindu students to the number of Christian students.
(b) the number of Muslim students to the total number of students.
Solution:
(a) 288/70 = 4/1 (9Hindu students)/(Christian students)
(b) 252/756 = 1/3 (Hindu students)/(Christian students)
Question 65:
When Chinmay visited chowpati at Mumbai on a holiday, he observed that the ratio of North Indian food stalls to South Indian food stalls is 5:4. If the total number of food stalls is 117, find the number of each type of food stalls.
Solution:
5/4 (North Indian)/(south Indian)
5x + 4x = 117
9x = 117
X = 117/9
X = 13
6x = 65, 4x = 52
65 North Indian and South Indian food stalls.
Question 66:
At the parking stand of Ramleela ground, Kartik counted that there are 115 cycles, 75 scooters and 45 bikes. Find the ratio of the number of cycles to the total number of vehicles.
Solution:
cycle/(Number of vehicle) 115/225 = 23/47
Question 67:
A train takes 2 hours to travel from Ajmer to Jaipur, which are 130km apart. How much time will it take to travel from Delhi to Bhopal which are 780km apart if the train is travelling at the uniform speed?
Solution:
130/2 = 780/x train is travelling at the uniform speed.
130x = 2 × 780
X = (2 × 780)/130
X = 12 hours take travel from Delhi to Bhopal.
Question 68:
The length and breadth of a school ground are 150m and 90m respectively, while the length and breadth of a mela ground are 210m and 126m, respectively. Are these measurements in proportion?
Solution:
Yes, these measurements are in proportion
150/90 = 5/3, 210/126 = 5/3
Question 69:
In Fig. 8.4, the comparative areas of the continents are given: What is the ratio of the areas of
(a) Africa to Europe
(b) Australia to Asia
(c) Antarctica to Combined area of North America and South America.
Solution:
(a) Number of squares that cover Africa is 26 number of squares that cover Europe is 10 26/10 = 13/5
(b) Number of squares that cover Australia is 8. Number of squares that cover Asia is 44 = 8/44 = 2/11
(c) Number of squares that cover Antarctica is 13. Number of squares the cover combined area of north America and south America is 35 = 13/35
Question 70:
A tea merchant blends two varieties of tea costing her Rs 234 and Rs 130 per kg in the ratio of their costs. If the weight of the mixture is 84kg, then find the weight of each variety of tea.
Solution:
(Variety 1)/(variety 2) = 234/130 = 9/5 is the ratio of cost variety of 1 be 9x and variety of 2 be 5x. Total weight of mixture = 84kg
9x + 5x = 84kg
14x = 84kg
X = 6kg
Weight of variety of 1 = 9 × 6 = 54kg
Weight of variety of 2 = 5 × 6 = 30 kg
Question 71:
An alloy contains only zinc and copper and they are in the ratio of 7:9. If the weight of the alloy is 8kg, then find the weight of copper in the alloy.
Solution:
zinc in the alloy = 7x
Copper in alloy = 9x
Total weight = 8kg
7x + 9x = 8kg
16x = 8kg
X = 1/2 kg
Copper in alloy = 9x
= 9 x 1/2 kg
= 9/2 kg
= 4 1/2 kg is the weight of copper in alloy.
Question 72:
In the following figure, each division represents 1cm:
Express numerically the ratios of the following distances:
(i) AC : AF
(ii) AG : AD
(iii) BF : AI
(iv) CE : DI
Solution:
(i) AC/AF = 2/5
(ii) AG/AD = 6/3 = 2/1
(iii) BF/AI = 4/8 = 1/2
(vi) CE/DI = 2/5
Question 73:
Find two numbers whose sum is 100 and whose ratio is 9 :16.
Solution:
9x + 16x = 100
25x = 100
X = 100/25
X = 4
9x = 9 × 4 = 36, 16x = 16 × 4 = 64
36 and 64 are these two numbers
Question 74:
In Fig. 8.6 (i) and Fig. 8.6 (ii), find the ratio of the area of the shaded portion to that of the whole figure:
Solution:
(i) 8/16 = 1/2 (for fig 8.6i) = (shaded portion)/(whole figure)
(ii) 8/16 = 1/2 (for fig 8.6ii) = (shaded portion)/(whole figure)
Question 75:
A typist has to type a manuscript of 40 pages. She has typed 30 pages of the manuscript. What is the ratio of the number of pages typed to the number of pages left?
Solution:
A typist has to type a manuscript of 40 pages
She has typed 30 pages
Left pages is 10
= (30 type pages)/(10 left pages)
= 3/1
Question 76:
In a floral design made from tiles each of dimensions 40cm by 60cm (See Fig. 8.7), find the ratios of:
(a) the perimeter of shaded portion to the perimeter of the whole design.
(b) the area of the shaded portion to the area of the unshaded portion.
Solution:
(a) Breadth = 40cm × 5 = 200cm
length = 60cm × 4 = 240cm
perimeter of whole region
= 240 + 200 + 240 + 200
= 880cm
(b) = (perimeter of shaded region)/(perimeter of whole region) = = 480cm/880cm = 6/11
Question 77:
In Fig. 8.8, what is the ratio of the areas of
(a) shaded portion I to shaded portion II?
(b) shaded portion II to shaded portion III?
(c) shaded portions I and II taken together and shaded portion III?
Solution:
Region I is in square shape, side = 5 cm
Area of the region I = 5 x 5
= 25 cm²
Region ii is in rectangular shape = l x b = 7cm × 5cm = 35 cm²
Area of ii region = Total area – (I region + III region)
= 10 x 10 cm² – 60 cm²
= 40 cm²
(a) (Shaded Portion I)/(Shaded portion II) = 25/40 = 5/8
(b) (region II)/(region III) = 40/35 = 8/7
(c) (region I + II)/(region III) = 65/35 = 13/7
Question 78:
A car can travel 240km in 15 litres of petrol. How much distance will it travel in 25 litres of petrol?
Solution:
= (240 km)/15 litre = 16/1
= 25 × 16
= 400 km distance travel.
Question 79:
Bachhu Manjhi earns Rs 24000 in 8 months. At this rate,
(a) how much does he earn in one year?
(b) in how many months does he earn Rs 42000?
Solution:
24000/8 = 3000 in one month
(a) 3000 × 12month = 36000 in one year
(b) 42000/3000 = 14 month
Question 80:
The yield of wheat from 8 hectares of land is 360 quintals. Find the number of hectares of land required for a yield of 540 quintals?
Solution:
(360 quintals)/(8 hectares) = 45 per hectares
540/45 = 12 number of hectares of land required for a yield of 540 quintals
Question 81:
The earth rotates 360° about its axis in about 24 hours. By how much degree will it rotate in 2 hours?
Solution:
(360°)/(24 hr) = 15° rotate in one hours
30° rotate in 2 hours
Question 82:
Shivangi is suffering from anaemia as haemoglobin level in her blood is lower than the normal range. Doctor advised her to take one iron tablet two times a day. If the cost of 10 tablets is Rs 17, then what amount will she be required to pay for her medical bill for 15 days?
Solution:
= 15days × 2 tablets
= 30 tablets are required
= tablet 10 = 17 Rs
= 17 × 3 = Rs 51 will be required to pay for her medical bill for 15 days.
Question 83:
The quarterly school fee in Kendriya Vidyalaya for Class VI is Rs 540. What will be the fee for seven months?
Solution:
Rs180 for one month
= 7 month = 7 × 180 Rs
= 7 months = Rs 1260
Question 84:
In an election, the votes cast for two of the candidates were in the ratio 5 : 7. If the successful candidate received 20734 votes, how many votes did his opponent receive?
Solution:
5/7 = (x opponent received )/(30734 successful candidates)
x = (5 × 20734)/7
= 5 × 2962
X = 14810 votes opponent receive
Question 85:
A metal pipe 3 metre long was found to weigh 7.6kg. What would be the weight of the same kind of 7.8m long pipe?
Solution:
metal pipe 3 metre long was found to weigh = 7.6kg
The weight of 1 meter long pipe = (7.6 kg)/3
= 7.8 x (7.6 kg)/3
= 19.76 kg is the weight of 7.8-meter-long pipe.
Question 86:
A recipe for raspberry jelly calls for 5 cups of raspberry juice and 2 1/2 cups of sugar. Find the amount of sugar needed for 6 cups of the juice?
Solution:
2 1/2 = 5/2 cup of sugar
(5/2)/5 = 1/2
1/2 cup of sugar for one raspberry jelly for 6 cups of juice 3cups of sugar needed.
Question 87:
A farmer planted 1890 tomato plants in a field in rows each having 63 plants. A certain type of worm destroyed 18 plants in each row. How many plants did the worm destroy in the whole field?
Solution:
= (1890 tomato plants )/(63 plants in each row)
= 210/7
= 30 rows
18 plants which are destroyed in each row = 18 × 30
= 540 plants destroy in the whole field
Question 88:
Length and breadth of the floor of a room are 5m and 3m, respectively forty tiles, each with area 1/16 m² are used to cover the floor partially. Find the ratio of the tiled and the non tiled portion of the floor.
Solution:
Each with area 21/16 m² are used to cover the floor partially
Area cover with the tiles = 40 × 1/16 m²
= 5/2 m²
Area of the floor = 5m × 3m = 15 m²
Non tile area = area of floor – area cover with tile
= (15 – 5/2) m²
= 25/2 m²
(Tile Area)/(Non tile Area) = (5/2 m²)/(25/2 m²) = 1:5
Question 89:
A carpenter had a board which measured 3m × 2m. She cut out a rectangular piece of 250cm × 90cm. What is the ratio of the area of cut out piece and the remaining piece?
Solution:
Area = 3m × 2m
Of a board = 6 m²
She cut out a rectangular piece
Area = 250cm × 90cm
= 22500 cm²
1 meter = 100 cm²
6 m² = 60,000 cm²
Remaining piece = 60000 cm² – 225000 cm²
= 37500 cm²
(Area of the cut out piece)/(Remaining piece) = 22500/37500
= 3/5
Thank You all the Students and Guardians who are always like our this page NCERT Exemplar Class 6 Maths Ratio and Proportion Solution. For any doubts comment us below.