NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion

NCERT Class 6 maths chapter 12 ratio and proportion topic 12.2 ratio

Question:1 In a class, there are 20 boys and 40 girls. What is the ratio of the number of boys to the number of girls?

Answer: number of boys = 20

number of girls = 40

$\frac{number \ of\ boys}{number\ of\ girls}=\frac{20}{40}=\frac{2}{4}=\frac{1}{2}$

So the required ratio is 1:2

Question:2 Ravi walks 6 km in an hour while Roshan walks 4 km in an hour What is the ratio of the distance covered by Ravi to the distance covered by Roshan?

Answer: The distance covered in one hour by Ravi = 6 Km

The distance covered in one hour by Roshan = 4 Km

$\frac{ The \ distance \ covered \ by \ Ravi }{ The \ distance \ covered \ by\ Roshan}=\frac{6}{4}=\frac{3}{2}$

So the required ratio is 3:2

Question:1 Saurabh takes 15 minutes to reach school from his house and Sachin takes one hour to reach school
from his house. Find the ratio of the time taken by Saurabh to the time taken by Sachin.

Answer: Time taken by Saurabh = 15 minutes

Time taken by Sachin= 1 hour = 60 minutes. To find ratios we have to convert the given quantities to the same units. Here we are expressing both the quantities in minutes

the ratio of the time taken by Saurabh to the time taken by Sachin= 15:60=1:4

Question:2 Cost of a toffee is 50 paise and cost of a chocolate is rupees 10. Find the ratio of the cost of a toffee to the cost of a chocolate.

Answer: Cost of toffee = 50 paise

cost of chocolate = 10 rupees

1rupee = 100 paise

Therefore, 10rupee = 1000 paise

So, the cost of chocolate = 1000 paise

the ratio of the cost of toffee to the cost of chocolate=50:1000=1:20

Question:3 In a school, there were 73 holidays in one year. What is the ratio of the number of holidays to the number of days in one year?

Answer: Number of holidays in a year = 73

Number of days in a year = 365

the ratio of the number of holidays to the number of days in one year= 1:5

Question:1 Find the ratio of number of notebooks to the number of books in your bag.

Answer: If there are 3 notebooks and 4 books in the bag then the ratio of the number of notebooks to the number of books =3:4

Question:2 Find the ratio of number of desks and chairs in your classroom.

Answer: If there are 8 desk and 32 chairs then the ratio of number of desks and chairs is 8:32=1:4

Question:3 Find the number of students above twelve years of age in your class. Then, find the ratio of the number of students with age above twelve years and the remaining students.

Answer: suppose there are 40 students in the class and 5 students are above 12 years, then there are 40-5=35 students below or equal to 12 years.

Then he ratio of the number of students with age above twelve years and the remaining students = 5:35=1:7

Question:4 Find the ratio of number of doors and the number of windows in your classroom.

Answer: If there are four windows and one door then the ratio of the number of doors and the number of windows =1:4

Question:5 Draw any rectangle and find the ratio of its length to its breadth.

Answer: Suppose a rectangle has length 10 cm and breadth of 7 cm then ratio of its length to its breadth=10:7

NCERT Class 6 maths chapter 12 ratio and proportion exercise 12.1

Question: 1(a) There aregirls andboys in a class. What is the ratio of number of girls to the number of boys?

Answer: Given,

Number of boys = 15

Number of girls = 20

So,

The ratio of the number of girls to the number of boys:

$=\frac{20}{15}=\frac{4}{3}=4:3$

Question: 1(b) There are girls and boys in a class. What is the ratio of number of girls to the total number of students in the class?

Answer: Given,

Number of boys = 15

Number of girls = 20

Total number of students = 15 + 20 = 35.

the ratio of the number of girls to the total number of students in the class:

$=\frac{20}{20+15}=\frac{20}{35}=\frac{4}{7}=4:7$

Question: 2(a) Out of students in a class, like football, like cricket and remaining like tennis. Find the ratio of Number of students liking football to number of students liking tennis.

Answer: Given,

Total Number of a student = 30

Number of students who like football = 6

Number of students who like cricket = 12

Number of remaining student wh play tennis = 30 - 6 - 12

= 12

Now,

The ratio of Number of students liking football to the number of students liking tennis:

$=\frac{6}{12}=\frac{1}{2}=1:2$

Question: 2 (b) Out of students in a class, like football, like cricket and remaining like tennis. Find the ratio of Number of students liking cricket to total number of students.

Answer: Given,

Total Number of a student = 30

Number of students who like football = 6

Number of students who like cricket = 12

Number of remaining student wh play tennis = 30 - 6 - 12

= 12

Now, The ratio of Number of students liking cricket to the total number of students:

$=\frac{12}{30}=\frac{6}{15}=\frac{2}{5}=2:5$

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.

Answer: From the figure, we can see that inside the rectangle,

Number of triangles = 3

Number of squares = 2

Number of circles = 2

So,

(a) The number of triangles to the number of circles inside the rectangle:

$\frac{3}{2}=3:2$

(b) Number of squares to all the figures inside the rectangle:

$\frac{2}{7}=2:7$

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: As we know,

$speed=\frac{distance}{time}$

So,

Speed of Hamid :

$speed=\frac{distance}{time}=\frac{9km}{1hour}=9km/h$

Speed of Akhtar :

$speed=\frac{distance}{time}=\frac{12km}{1hour}=12km/h$

Hence, the ratio of the speed of Hamid to the speed of Akhtar:

$\frac{9}{12}=\frac{3}{4}=3:4$ .

Question: 5 Fill in the following blanks:

$\frac{15}{18}=\frac{\square }{6}=\frac{10}{\square}=\frac{\square }{30}$ [Are these equivalent ratios?]

Answer: Equating all the fraction, we get

$\frac{15}{18}=\frac{5 }{6}=\frac{10}{12}=\frac{25 }{30}$

Yes, They are equivalent ratios.

Question: 6 Find the ratio of the following :

(a) $81 \; to \; 108$

(b) $98 \; to \; 63$

(d) minutes to minutes

Answer: (a)Ratio of $81 \; to \; 108$

$= \frac{81}{108}=\frac{27}{36}=\frac{3}{4}=3:4$

(b) Ratio of $98 \; to \; 63$

$= \frac{98}{63}=\frac{14}{9}=14:9$

$= \frac{33}{121}=\frac{3}{11}=3:11$

(d) The ratio of minutes to minutes

$= \frac{30}{45}=\frac{6}{9}=\frac{2}{3}=2:3$

Question: 7 Find the ratio of the following:

(a) minutes to hours

(b) $40\; cm$ to $1.5 \; cm$

(d) $500\; mL$ to $2\; litres$

Answer: (a) minutes to hours

As we know,

$1 \:hour = 60\:minutes$

So,

$1.5 \:hour =1.5\times 60=90\:minutes$

Hence the ratio of minutes to hours:

$\frac{30}{90}=\frac{3}{9}=\frac{1}{3}=1:3$

(b) $40\; cm$ to

As we know,

$1 \:m= 100\:cm$

So,

$1.5 \:m=1.5\times 100=150\:cm$

Hence the ratio of $40\; cm$ to $1.5 \:m=1.5\times 100=150\:m$

$\frac{40}{150}=\frac{4}{15}=4:15.$

As we know,

$1 \:rupee= 100\:paise$

Hence the ratio of paise to

$\frac{55}{100}=\frac{11}{20}=11:20$

(d) $500\; mL$ to $2\; litres$

As we know,

$1 \:litre= 1000\:mL$

$2 \:litre= 2\times1000=2000\:mL$

Hence the ratio of $500\; mL$ to $2\; litres$ :

$\frac{500}{2000}=\frac{1}{4}=1:4$

Question: 8(a) In a year, Seema earns and saves . Find the ratio of Money that Seema earns to the money she saves.

Answer: Money that Seema earns =

the money that Seema saves.=

So, The ratio of Money that Seema earns to the money she saves:

$=\frac{150000}{50000}=\frac{3}{1}=3:1$ .

Hence the required ratio is 3:1.

Question: 8(b) In a year, Seema earns and saves . Find the ratio of Money that she saves to the money she spends.

Answer: Money that Seema earns =

the money that Seema saves.=

The amount of money Seema spends = $Rs\: 150,000-Rs\:50,000=100,000.$

So, The ratio of Money that she saves to the money she spends.

$=\frac{50000}{100000}=\frac{1}{2}=1:2$ .

Hence the required ratio is 1:2.

Question: 9 There are teachers in a school of students. Find the ratio of the number of teachers to the number of students.

Answer: Given

Number of Teacher = 102

Number of students = 3300

So, the ratio of the number of teachers to the number of students:

$\frac{102}{3300}=\frac{17}{550}=17:550.$

Hence the required ratio is 17 : 550

Question: 10 In a college, out of students, 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.

Answer: Given

Total number of students = 4320

Number of girls = 2300

The number of boys = 4320 - 2300

= 2020

So,

the ratio of

(a) Number of girls to the total number of students:

$=\frac{2300}{4320}=\frac{230}{432}=\frac{115}{216}=115:216$

(b) The number of boys to the number of girls:

$=\frac{2020}{2300}=\frac{101}{115}=101:115$

$=\frac{2020}{4320}=\frac{101}{216}=101:216$

Question: 11 Out of students in a school, opted basketball, 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.

Answer: Total number of students = 1800

Number of students who opted for basketball = 750

Number of students who opted for cricket= 800

Number of students who opted for Table Tennis = 1800 - 750 - 800

= 250

Now,

The ratio of

(a) The number of students who opted basketball to the number of students who opted table tennis:

$\frac{750}{250}=\frac{3}{1}=3:1$

(b) The number of students who opted cricket to the number of students opting basketball:

$\frac{800}{750}=\frac{16}{15}=16:15$

$\frac{750}{1800}=\frac{5}{12}=5:12$

Question: 12 Cost of a dozen pens is and cost of ball pens is . Find the ratio of the cost of a pen to the cost of a ball pen.

Answer: Cost of 12 ( a dozen ) pens = Rs 180

Cost of 1 pen = 180 / 12 = Rs 15

Cost of 8 ball pens = Rs 56

Cost of 1 ball pen = 56 / 8 = Rs 7

So,

the ratio of the cost of a pen to the cost of a ball pen:

$=\frac{15}{7}=15:7$ .

Question: 13 Consider the statement: Ratio of breadth and length of a hall is Complete the following table that shows some possible breadths and lengths of the hall.

Answer: Given Breadth and Length is in proportion

Maintaining that proportion, we get.

Breadth of the hall (in m)	10	20	40
Length of the hall (in m)	25	50	100

Question: 14 Divide pens between Sheela and Sangeeta in the ratio of

Answer: Given

Total number of pens = 20

The required ratio between Sheela and Sangeeta = 3 : 2

On adding the numbers in ratio we get 3 + 2 = 5.

Sheela will have 3/5 of the total pen :

$=\frac{3}{5}\times20=3\times4=12$

and Sangeeta will have 2/5 of the total pen:

$=\frac{2}{5}\times20=2\times4=8$

Hence Sheela will get 12 pens and Sangeeta will get 8 pens.

Question: 15 Mother wants to divide between her daughters Shreya and Bhoomika in the ratio of their ages. If age of Shreya is years and age of Bhoomika is years, find how much Shreya and Bhoomika will get.

Answer: Given,

Total money = Rs 36

Bhoomikas age = 12 years

Shreya's age = 15 years.

Now According to the question,

we are dividing 36 in ratio 15 : 12.

So, the sum of number in ratio = 15 + 12 = 27

Hence

amount of money Shreya gets:

$=\frac{15}{27}\times36$

$=\frac{15}{3}\times4$

$=5\times4$

Rs .

Amount of money Sangeeta gets :

$=\frac{12}{27}\times36=\frac{12}{3}\times4=4\times4=16.$

Hence Shreya and Sangeeta get 20 Rs and 16 Rs respectively.

Question:1 6 Present age of father is years and that of his son is 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 years old.

(d) Age of father to the age of son when father was years old.

Answer: Given, Present age of father = years and that of his son = years.

The ratio of

(a) Present age of father to the present age of the son:

$=\frac{42}{14}=\frac{3}{1}=3:1$

(b) Age of the father to the age of the son, when the son was 12 years old:

$=\frac{42-2}{14-2}=\frac{40}{12}=\frac{10}{3}=10:3$

$=\frac{42+10}{14+10}=\frac{52}{24}=\frac{13}{6}=13:6.$

(d) Age of father to the age of son when father was 30 years old.

$=\frac{42-12}{14-12}=\frac{30}{2}=\frac{15}{1}=15:1$

NCERT Class 6 maths chapter 12 ratio and proportion topic 12.3 proportion

Question: Check whether the given ratios are equal, i.e. they are in proportion. If yes, then write them in the proper form.
1. 1 : 5 and 3 : 15
2. 2 : 9 and 18 : 81
3. 15 : 45 and 5 : 25
4. 4 : 12 and 9 : 27
5. ` 10 to ` 15 and 4 to 6

Answer: 1. 1 : 5 and 3 : 15

$\frac{3}{15}=\frac{3}{3\times5}=\frac{1}{5}$

So the ratios are in proportion
2. 2 : 9 and 18 : 81

$\frac{2}{9}=\frac{2\times9}{9\times9}=\frac{18}{81}$

So So the ratios are in proportion
3. 15 : 45 and 5 : 25

$\\\frac{15}{45}=\frac{1}{3}\\\frac{5}{25}=\frac{1}{5}$

The given ratios are not equal, so they are not in proportion
4. 4 : 12 and 9 : 27

$\\\frac{4}{12}=\frac{1}{3}\\\frac{9}{27}=\frac{1}{3}$

The given ratios are equal, so they are in proportion
5. ` 10 to ` 15 and 4 to 6

$\\\frac{10}{15}=\frac{2}{3}\\\frac{4}{6}=\frac{2}{3}$

The given ratios are equal, so they are in proportion

NCERT class 6 maths chapter 12 ratio and proportion exercise 12.2

Question: 1 Determine if the following are in proportion.

(a)

(b)

(c)

(d)

(e)

(f)

Answer: (a)

$\frac{15}{45}=\frac{1}{3}........(1)$

$\frac{40}{120}=\frac{1}{3}........(2)$

Since (1) and (2) are equal, Yes they are in proportion.

(b)

$\frac{33}{121}=\frac{3}{11}........(1)$

$\frac{9}{96}=\frac{3}{32}........(2)$

Since (1) and (2) are not equal, No they are not in proportion.

(c)

$\frac{24}{28}=\frac{6}{7}........(1)$

$\frac{36}{48}=\frac{3}{4}........(2)$

Since (1) and (2) are not equal, No they are not in proportion.

(d)

$\frac{32}{48}=\frac{2}{3}........(1)$

$\frac{70}{210}=\frac{1}{3}........(2)$

Since (1) and (2) are not equal, No they are not in proportion.

(e)

$\frac{4}{6}=\frac{2}{3}........(1)$

$\frac{8}{12}=\frac{2}{3}........(2)$

Since (1) and (2) are equal, Yes they are in proportion.

(f)

$\frac{33}{44}=\frac{3}{4}........(1)$

$\frac{75}{100}=\frac{3}{4}........(2)$

Since (1) and (2) are equal, Yes they are in proportion.

Question: 2 Write True ( T ) or False ( F ) against each of the following statements :

(a)

(b)

(c)

(d)

(e)

(f)

Answer: (a)

$\frac{16}{24}=\frac{2}{3}.......(1)$

$\frac{20}{30}=\frac{2}{3}.......(2)$

As we can see (1) and (2) are equal So, They are in proportion.

Hence the statement is True.

(b)

$\frac{21}{6}=\frac{7}{2}.......(1)$

$\frac{35}{10}=\frac{7}{2}.......(2)$

As we can see (1) and (2) are equal So, They are in proportion.i.e

. .

Hence the statement is True.

(c)

$\frac{12}{18}=\frac{2}{3}.......(1)$

$\frac{28}{12}=\frac{7}{3}.......(2)$

As we can see (1) and (2) are not equal So, They are not in proportion.

Hence the statement is False.

(d)

$\frac{8}{9}=\frac{8}{9}.......(1)$

$\frac{24}{27}=\frac{8}{9}.......(2)$

As we can see (1) and (2) are equal So, They are in proportion.i.e.

Hence the statement is True.

(e)

$\frac{5.2}{3.9}=\frac{4}{3}.......(1)$

$\frac{3}{4}=\frac{3}{4}.......(2)$

As we can see (1) and (2) are not equal So, They are not in proportion.

Hence the statement is False.

(f)

$\frac{0.9}{0.36}=\frac{10}{4}.......(1)$

$\frac{10}{4}=\frac{10}{4}.......(2)$

As we can see (1) and (2) are equal So, They are in proportion.i.e.

Hence the statement is True.

Question: 3 Are the following statements true?

(a) persons : persons =

(b) litres : litres = $5\; kg:10\; kg$

(d) $32\; m:64\; m=6\; sec:12\; sec$

(e) $45\; km:60\; km=$ hours : hours

Answer: (a) persons : persons =

$\frac{40}{200}=\frac{1}{5}.........(1)$

$\frac{15}{75}=\frac{1}{5}.........(2)$

As we can see (1) is equal to (2), They are in proportion.

Hence The statement is True.

(b) litres : litres = $5\; kg:10\; kg$

$\frac{7.5}{15}=\frac{1}{2}.........(1)$

$\frac{5}{10}=\frac{1}{2}.........(2)$

As we can see (1) is equal to (2), They are in proportion.

Hence The statement is True.

$\frac{99}{45}=\frac{11}{5}.........(1)$

$\frac{44}{20}=\frac{11}{5}.........(2)$

As we can see (1) is equal to (2), They are in proportion.

Hence The statement is True.

(d) $32\; m:64\; m=6\; sec:12\; sec$

$\frac{32}{64}=\frac{1}{2}.........(1)$

$\frac{6}{12}=\frac{1}{2}.........(2)$

As we can see (1) is equal to (2), They are in proportion.

Hence The statement is True.

(e) $45\; km:60\; km=$ hours : hours

$\frac{45}{60}=\frac{3}{4}.........(1)$

$\frac{12}{15}=\frac{4}{5}.........(2)$

As we can see (1) is not equal to (2), They are not in proportion.

Hence the statement is False.

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) litres : litres and bottles : bottles

(d) $200\; mL:2.5\; litre\; and\; Rs.4:Rs.50$

Answer: (a) $25\; cm:1\; m\; and\; Rs.40:Rs.160$

$\frac{25}{100}=\frac{1}{4}...........(1)$

$\frac{40}{160}=\frac{1}{4}...........(2)$

As we can see (1) and (2) are equal, they are in proportion.

Middle Terms: 1 m and Rs 40

Extreme Terms: 25 cm and Rs 160.

(b) litres: litres and bottles : bottles

$\frac{39}{65}=\frac{3}{5}...........(1)$

$\frac{6}{10}=\frac{3}{5}...........(2)$

As we can see (1) and (2) are equal, they are in proportion.

Middle Terms: 65 litres and 6 bottles

Extreme Terms: 39 litres and 10 bottles.

$\frac{2}{80}=\frac{1}{40}...........(1)$

$\frac{25}{626}=\frac{1}{25}...........(2)$

As we can see (1) and (2) are not equal, they are not in proportion.

(d) $200\; mL:2.5\; litre\; and\; Rs.4:Rs.50$

$\frac{200}{2500}=\frac{2}{25}...........(1)$

$\frac{4}{50}=\frac{2}{50}...........(2)$

As we can see (1) and (2) are equal, they are in proportion.

Middle Terms: 2.5 litres and Rs 4

Extreme Terms:200 mL and Rs 50.

NCERT class 6 maths chapter 12 ratio and proportion topic 12.4 unitary method

Question:2 Read the table and fill in the boxes

Answer:

Time	Distance travelled by Karan	Distance travelled by Kriti
2 hours	8	6
1 hour	4	3
4 hours	16	12

Distance travelled in 1 hour will be half of the distance travelled in 2 hours. Distance travelled in 4 hours will be double of the distance travelled in 2 hours

NCERT class 6 maths chapter 12 ratio and proportion exercise 12.3

Question: 1 If the cost of $7\; m$ of cloth is find the cost of $5\; m$ of cloth.

Answer: Given,

Cost of 7 m cloth = Rs 1470

Cost of 1 m cloth :

$=\frac{1470}{7}=Rs\:210$

So,

Cost of 5 m cloth :

$=Rs\:210\times5=Rs\:1050$

Hence the cost of 5 m cloth is Rs 1050.

Question: 2 Ekta earns in days. How much will she earn in days?

Answer: Given

Amount of money earned in 10 days:

$=Rs \:3000$

So,

Amount of money earned in 1 day :

$=\frac{3000}{10}=Rs\:300$

So,

Amount of Money earned in 30 days :

$30\times\:300=Rs\:9000$

Hence Ekta will earn 9000 Rs in 30 days.

Question: 3 If it has rained $276\; mm$ in the last $3\; days,$ 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: Given

The measure of rain in 3 days :

$=276\; mm$

So,

The measure of rain in 1 day :

$=\frac{276}{3}=92\; mm$

And Hence,

The measure of rain in 7 days :

$=7\times92=644\; mm$

Therefore, 644 mm rain will fall in a week.

Question: 4(a) Cost of 5 kg of wheat is

What will be the cost of $8\; kg$ of wheat?

Answer: Given,

The cost of 5 kg of wheat:

$=Rs \:91.50$

So,

The cost of 1 kg of wheat :

$=\frac{91.50}{5}=Rs\:18.30$

And Hence,

The cost of 8 kg of wheat :

$=8\times\:18.30=Rs\:146.40$

Therefore, the cost of 8 kg of wheat is Rs 146.40.

Question: 4(b) Cost of $5\; kg$ of wheat is

What quantity of wheat can be purchased in

Answer: Given,

The cost of 5 kg of wheat:

$=Rs \:91.50$

So,

The cost of 1 kg of wheat :

$=\frac{91.50}{5}=Rs\:18.30$

So, The amount of wheat which can be bought in Rs 183:

$=\frac{183}{18.3}=10kg$

Hence 10 kg of wheat can be bought in Rs 183.

Question: 5 The temperature dropped degree celsius in the last 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 :

So, Temperature drop in 1 day :

$=\frac{15}{30}=\frac{1}{2}=0.5^o$

And Hence, The Temperature drop in 10 days :

$=10\times0.5^o=5^o$

Hence if the temperature rate remains the same, there will be a drop of 5 degrees in the next 10 days.

Question: 6 Shaina pays as rent for 3 months. How much does she has to pay for a whole year, if the rent per month remains same?

Answer: Given

Rent of 3 months :

$=Rs \:15000$

So,

Rent of 1 month :

$=\frac{15000}{3}=Rs \:5000$

And Hence Using unity principle

Rent of 1 year (12 months ) :

$=12\times\:5000=Rs\:60000$

Therefore, The total rent for one year is Rs 60000.

Question: 7 Cost of 4 dozen bananas is How many bananas can be purchased for

Answer: Given,

Number of bananas we can buy in Rs 180 = 4 dozen = 12 x 4 = 48

The number of bananas we can buy in Rs 1 :

$=\frac{48}{180}=\frac{4}{15}$

So, the number of bananas we can buy in Rs 90:

$=90\times\frac{4}{15}=24$

Hence we can buy 24 bananas in Rs 90.

Question: 8 The weight of 72 books is $9\; kg.$ What is the weight of 40 such books?

Answer: Given,

The weight of 72 books = 9 kg

So, The weight of 1 book :

$=\frac{9}{72}=\frac{1}{8}kg$

And hence,

The weight of 40 such books:

$=40\times\frac{1}{8}=5kg$

Hence, the weight of 40 books will be 5 kg.

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: Given

Diesel requires for covering 594 km = 108 litres

So,

Diesel requires for covering 1 km :

$=\frac{108}{594}=\frac{2}{11}L$

And hence,

Diesel requires for covering 1650 km :

$=1650\times\frac{2}{11}=300L$

Hence The truck will require 300 litres of diesel to cover the distance of 1650 km.

Question: 10 Raju purchases pens for and Manish buys pens for Can you say who got the pens cheaper?

Answer: Cost of Raju's 10 pens = Rs 150

Cost of Raju's 1 pen :

$=\frac{150}{10}=Rs \:15$

And

Cost of Manish's 7 pens = Rs 84

Cost of Manish's 1 pen;

$=\frac{84}{7}=Rs \:12$

As we can see the cost of Raju's 1 pen is 15 and the cost of Manish's 1 pen is 12, Manish got the pen at a cheaper rate.

Question: 11 Anish made runs in overs and Anup made runs in overs. Who made more runs per over?

Answer: Anish's Case:

runs in 6 overs = 42

So, runs in 1 over:

$=\frac{42}{6}=7$

Anup's Case:

Run in 7 overs = 63

So, Runs in 1 over :

$=\frac{63}{7}=9$

As we can see Anup made more runs per over.