Telangana SCERT Class 6 Maths Chapter 11 Solution – Ratio and Proportion. Here in this post we provides Class 6 Maths Ratio and Proportion Telangana State Board Solution. Telangana State Board English Class VI Medium Students can download this Solution to Solve out Improve Your Learning Questions and Answers.
Telangana State Board Class 6 Maths Chapter 11 Ratio and Proportion Solution:
EXERCISE – 11.1
1.) Complete the following table.
ANSWER:
From table we have to find ratio of given pictures.
ii) First Quantity = 7 balls
Second Quantity = 11 balls
Ratio of First Quantity to Second Quantity = 7: 11
iii) First Quantity = 2 cars
Second Quantity = 3 cars
Ratio of First Quantity to Second Quantity = 2: 3
iv) First Quantity = 5 cups
Second Quantity = 8 cups
Ratio of First Quantity to Second Quantity = 5:8
v) First Quantity = 3 Butterflies
Second Quantity = 5 Butterflies
Ratio of First Quantity to Second Quantity = 3:5
2.) Compare:
(i) Number of blue coloured squares is ________ times of the number of red colour squares.
ANSWER:
Number of blue coloured squares = 6
Number of red colour squares = 3
Number of blue coloured squares is two (2) times of the number of red colour squares.
(ii) Number of red coloured squares is ________ times of the number of blue coloured squares.
ANSWER:
Number of red coloured squares = 3
Number of blue coloured squares = 6
Number of red coloured squares is 1/2 times of the number of blue coloured squares.
(iii) Find the ratio of number of blue squares to the number of red squares.
ANSWER:
Number of red coloured squares = 3
Number of blue coloured squares = 6
We have to find ratio of number of blue squares to the number of red squares
Ratio of number of blue squares to the number of red squares = 6: 3
Ratio of number of blue squares to the number of red squares = 2:1
3.) Solve the following:
(i) A milk man adds 250 ml of water to 1 litre of milk. Find the ratio of water to milk.
ANSWER:
Given,
A milk man adds 250 ml of water to 1 litre of milk.
We know,
1 litre = 1000 ml
We have to find the ratio of water to milk.
The ratio of water to milk = 250 ml: 1000 ml
The ratio of water to milk = 1:4
(ii) Satya’s mother bought 4 kg pulses and 50g chilli powder. Find the ratio of weights of chilli powder to pulses. What is the ratio of weights of the pulses to chilli powder?
ANSWER:
Given, Satya’s mother bought 4 kg pulses and 50g chilli powder.
We have to find the ratio of weights of chilli powder to pulses.
We have to find the ratio of weights of the pulses to chilli powder.
We know,
1 kg = 1000 gm.
4 kg = 4000 gm.
The ratio of weights of chilli powder to pulses = 50 gm.: 4000 gm.
The ratio of weights of chilli powder to pulses = 1:80
Now,
The ratio of weights of the pulses to chilli powder = 4000 gm.: 50 gm.
The ratio of weights of the pulses to chilli powder = 80:1
(iii) Rani takes 30 minutes to reach school from home. Ismail takes ½ an hour to cover the same distance. Find the ratio of time taken by Rani to the time taken by Ismail.
ANSWER:
Given,
Rani takes 30 minutes to reach school from home.
Ismail takes ½ an hour to cover the same distance.
We have to find the ratio of time taken by Rani to the time taken by Ismail.
We know,
1 hour = 60 minute
1/2 hour = 30 minute.
The ratio of time taken by Rani to the time taken by Ismail = 30 minute: 30 minute
The ratio of time taken by Rani to the time taken by Ismail = 1:1
EXERCISE – 11.2
1.) Express the following ratios in their simplest form.
(i) 2:3
ANSWER:
We know,
A ratio is said to be in the simplest form or in the lowest terms when it is written in terms of whole numbers with no common factors other than 1.
2:3 = 2/3 in their simplest form.
(ii) 16:20
ANSWER:
We know,
A ratio is said to be in the simplest form or in the lowest terms when it is written in terms of whole numbers with no common factors other than 1.
16:20 we divide both by 4 we get 4/5
16:20 = 4/5 this in the simplest form.
(iii) 5:6
ANSWER:
We know,
A ratio is said to be in the simplest form or in the lowest terms when it is written in terms of whole numbers with no common factors other than 1.
5:6 = 5/6 in their simplest form.
(iv) 20:60
ANSWER:
We know,
A ratio is said to be in the simplest form or in the lowest terms when it is written in terms of whole numbers with no common factors other than 1.
20:60 we divide both by 20 we get 1/3
20:60 = 1/3 this in the simplest form.
(v) 8:15
ANSWER:
We know,
A ratio is said to be in the simplest form or in the lowest terms when it is written in terms of whole numbers with no common factors other than 1.
8:15 = 8/15 in their simplest form.
(vi) 19 : 2
ANSWER:
We know,
A ratio is said to be in the simplest form or in the lowest terms when it is written in terms of whole numbers with no common factors other than 1.
19 : 2 = 19/2 in their simplest form.
2.) A bag contains 20kg of rice and another bag contains 60 kg of wheat. Find the ratio of the amount of rice to that of wheat? What is the ratio of rice to the total weight?
ANSWER:
Given,
A bag contains 20kg of rice and another bag contains 60 kg of wheat.
We have to find the ratio of the amount of rice to that of wheat.
We have to find the ratio of rice to the total weight.
Now,
The ratio of the amount of rice to that of wheat = 20kg of rice: 60 kg of wheat
The ratio of the amount of rice to that of wheat = 1:3
Now,
Total weight = 20kg of rice + 60 kg of wheat = 80 kg.
The ratio of rice to the total weight = 20kg of rice: 80 kg.
The ratio of rice to the total weight = 1:4
3.) There are 32 students in a class of which 12 are girls. Find:
(i) The ratio of number of boys to number of girls
ANSWER:
Given,
There are 32 students in a class of which 12 are girls.
Number of boys = 32 – 12
Number of boys = 20
Now,
The ratio of number of boys to number of girls = 20:12
We divide by 4 we get,
The ratio of number of boys to number of girls = 5:3
(ii) The ratio of number of boys to total number of students
ANSWER:
Given,
There are 32 students in a class of which 12 are girls.
Number of boys = 20
The ratio of number of boys to total number of students = 20: 32
We divide by 4 we get,
The ratio of number of boys to total number of students = 5:8
(iii) The ratio of number of girls to total number of students.
ANSWER:
Given,
There are 32 students in a class of which 12 are girls.
Number of boys = 20
The ratio of number of girls to total number of students = 12: 32
We divide by 4 we get,
The ratio of number of girls to total number of students = 3:8
4.) Draw a four sided closed figure and divide it in to some number of equal parts. Shade the figure with any colour so that the ratio of shaded parts to unshaded parts 1: 3. Draw two more different figures and do the same.
ANSWER:
Here we have to draw four sided closed figure and divide it in to some number of equal parts.
The ratio of shaded parts to unshaded parts 1: 3.
5.) Imran bought 2 liters of oil and Vijay bought 500ml of oil. Find the ratio of quantities of oil bought by Imran to oil bought by Vijay.
ANSWER:
Given,
Imran bought 2 liters of oil and Vijay bought 500ml of oil.
We have to find the ratio of quantities of oil bought by Imran to oil bought by Vijay.
We know,
1 liter = 1000 ml
2 liters = 2000 ml
The ratio of quantities of oil bought by Imran to oil bought by Vijay = 2000: 500
The ratio of quantities of oil bought by Imran to oil bought by Vijay = 4:1
6.) Weight of Abraham is 20 kg and his father’s weight is 60kg. Find the ratio of weight of Abraham and his father. Express it in the simplest form.
ANSWER:
Given,
Weight of Abraham is 20 kg and his father’s weight is 60kg.
We have to find the ratio of weight of Abraham and his father. Also express it in the simplest form.
The ratio of weight of Abraham and his father = 20 kg: 60kg.
The ratio of weight of Abraham and his father = 1:3
Simplest form is 1/3
7.) Ramu spent 2/5th of his money on a story book. Find the ratio of money spent to the money with him at the beginning.
ANSWER:
Given,
Ramu spent 2/5th of his money on a story book.
We have to find the ratio of money spent to the money with him at the beginning.
Total 5 money out of 2 money spent on story book.
The ratio of money spent to the money with him at the beginning = 2:5
EXERCISE – 11.3
1.) A bag of 25 marbles is shared between Rahul and Kiran in the ratio 2: 3
(i) How many marbles does Kiran receive?
ANSWER:
Given,
A bag of 25 marbles is shared between Rahul and Kiran in the ratio 2: 3
Let,
Marbles shared between Rahul and Kiran are 2x and 3x respectively.
25 marbles = 2x + 3x
25 marbles = 5x
X = 25/5
X = 5
Marbles shared to Kiran = 3x = 3 x 5 = 15 marbles
(ii) How many marbles does Rahul receive?
ANSWER:
Let,
Marbles shared between Rahul and Kiran are 2x and 3x respectively.
25 marbles = 2x + 3x
25 marbles = 5x
X = 25/5
X = 5
Marbles shared to Rahul = 2x = 2 x 5 = 10 marbles
2.) A point X on AB = 14 cm divides it in the ratio 3 : 4. Find the length of AX and XB.
ANSWER:
Given,
A point X on AB = 14 cm divides it in the ratio 3 : 4.
We have to find the length of AX and XB.
Let,
AX and XB are 3x and 4x respectively.
AB = AX + XB
14 = 3x + 4x
14 = 7x
X = 2
Length of AX = 3x = 3 x 2 = 6cm
Length of XB = 4x = 4 x 2 = 8cm
3.) Geetha and Laxmi won Rs.1050 in a game. They agreed to share the amount in the ratio of 3:4. How much does each person receive?
ANSWER:
Given,
Geetha and Laxmi won Rs.1050 in a game.
Share the amount in the ratio of 3:4.
We have to find how much does each person receive.
Let, Share amount between Geetha and Laxmi is 3x and 4x respectively.
Rs.1050 = 3x + 4x
Rs.1050 = 7x
X = 1050 / 7
X = 150
Amount receive by Geetha = 3x = 3 x 150 = Rs.450
Amount receive by Laxmi = 4x = 4 x 150 = Rs.600
4.) Divide Rs. 3600 between Satya and Vishnu in the ratio of 3:5.
ANSWER:
Here, we have to divide Rs. 3600 between Satya and Vishnu in the ratio of 3:5.
Let, Rs. 3600 between Satya and Vishnu are 3x and 5x respectively.
Rs. 3600 = 3x + 5x
Rs. 3600 = 8x
X = 450
Amount receive by Satya = 3x = 3 x 450 = Rs.1350
Amount receive by Vishnu = 5x = 5 x 450 = Rs.2250
5.) Two numbers are in the ratio 5:6. If the sum of the numbers is 132, find the two numbers.
ANSWER:
Given,
Two numbers are in the ratio 5:6
The sum of the numbers is 132.
We have to find the two numbers.
The two numbers are 5x and 6x respectively.
Sum of the numbers is 132
5x + 6x = 132
11x = 132
X = 132/11
X = 12
1st number = 5x = 5 x 12 = 60
2nd number = 6x = 6 x 12 = 72
6.) Estimate the ratio in which X divides AB and then check your estimation by measuring it.
ANSWER:
By estimating and measuring,
The ratio in which X divides AB is 1:1
7.) The income and savings of an employee are in the ratio 11:2. If his expenditure is Rs.5346, then find his income and savings.
ANSWER:
Given,
The income and savings of an employee are in the ratio 11:2.
Let, income and savings of an employee are 11x and 2x.
If his expenditure is Rs.5346.
We have to find his income and savings.
We know,
Saving = income – expenditure
Expenditure = income – saving
Expenditure = 11 – 2
Expenditure = 9 ratio.
But expenditure is Rs.5346.
1 ratio = Rs.5346 / 9
1 ratio = 594
Income = 11x = 11 x 594 = Rs.6534
Saving = 2x = 2 x 594 = Rs.1088
EXERCISE – 11.4
1.) If three apples cost Rs.45, how much would five apples cost?
ANSWER:
Given,
Three apples cost Rs.45
We have to find five apples cost.
We find first find cost of 1 apple.
Cost of 1 apple = Rs.45 / 3
Cost of 1 apple = Rs. 15
Now,
Cost of 5 apples = Rs. 15 x 5
Cost of 5 apples = Rs.75
2.) Laxmi bought 7 books for a total of Rs. 56. How much would she pay for just 3 books?
ANSWER:
Given,
Laxmi bought 7 books for a total of Rs. 56
We have to find how much would she pay for just 3 books.
We find first find cost of 1 book.
Cost of 1 book = Rs. 56 / 7
Cost of 1 book = Rs.8
Cost of 3 book = Rs. 8 x 3
Cost of 3 book = Rs.24
Laxmi pay Rs.24 for just 3 books.
3.) Reena wants to prepare vegetable pulao. She needs 300 grams of rice. If she has to feed 4 people. How much of rice is needed if the same pulao is prepared for 7 people?
ANSWER:
Given,
Reena needs 300 grams of rice for feed 4 people.
We have to find how much of rice is needed if the same pulao is prepared for 7 people.
We find first how much rice needed to 1 people.
Rice needed to 1 people = 300 grams / 4
Rice needed to 1 people = 75 grams.
Rice needed for 7 people = 75 grams x 7
Rice needed for 7 people = 525 grams.
4.) The cost of 16 chairs is Rs.3600. Find the number of chairs that can be purchased for Rs.4500.
ANSWER:
Given,
The cost of 16 chairs is Rs.3600.
We have to find the number of chairs that can be purchased for Rs.4500.
We 1st find cost of 1 chair.
Cost of 1 chair = Rs.3600 / 16
Cost of 1 chair = Rs. 225
The number of chairs that can be purchased for Rs.4500 = Rs.4500 / Cost of 1 chair
The number of chairs that can be purchased for Rs.4500 = Rs.4500 / Rs. 225
The number of chairs that can be purchased for Rs.4500 = 20 chairs
5.) A train moving at a constant speed covers a distance of 90 km. in 2 hours. Find the time taken by the train to cover a distance of 540 km at the same speed.
ANSWER:
Given,
Train moving at a constant speed covers a distance of 90 km. in 2 hours.
We have to find the time taken by the train to cover a distance of 540 km at the same speed.
We 1st find distance travel in 1 hour.
Distance travel in 1 hour = 90 km / 2 hours.
Distance travel in 1 hour = 45 km.
Now,
The time taken by the train to cover a distance of 540 km = 540 km / Distance travel in 1 hour
The time taken by the train to cover a distance of 540 km = 540 km /45 km.
The time taken by the train to cover a distance of 540 km = 12 hours.
6.) The income of Kumar for 3 months is Rs.15000. If his monthly income remains the same then,
(i) How much will he earn in 5 months?
ANSWER:
Given,
The income of Kumar for 3 months is Rs.15000.
We have to find how much will he earn in 5 months.
We 1st find salary of 1st month
Salary of 1st month = Rs.15000 / 3
Salary of 1st month = Rs.5000
Salary of 5 month = Rs.5000 x 5
Salary of 5 month = Rs.25000
(ii) In how many months will he earn Rs. 95000?
ANSWER:
We have to find in how many months will he earn Rs. 95000.
Months will require to earn Rs.95000 = Rs.95000 / Salary of 1st month
Months will require to earn Rs.95000 = Rs.95000 / Rs.5000
Months will require to earn Rs.95000 = 19 months.
7.) If the cost of 7 meters of cloth is Rs 294, find the cost of 5m of cloth.
ANSWER:
Given,
The cost of 7 meters of cloth is Rs 294
We have to find cost of 5m of cloth.
We 1st find cost of 1 m of cloth.
Cost of 1 m of cloth = Rs 294 / 7
Cost of 1 m of cloth = Rs.42
Now,
Cost of 5 m of cloth = Rs.42 x 5
Cost of 5 m of cloth = Rs.210
8.) A farmer has sheep and cows in the ratio 8 : 3.
(i) How many sheep has the farmer, if he has 180 cows?
ANSWER:
Given,
A farmer has sheep and cows in the ratio 8: 3
Let, sheep and cows are 8x and 3x respectively.
We have to find how many sheep has the farmer, if he has 180 cows.
Ratio of cows is 3x which is 180
1 ratio = 180 / 3
1 ratio= x = 60
Now,
Ratio of sheep is 8x.
Number of sheep = 8 x 60 = 480 sheep
(ii) Find the ratio of the number of sheep to the total number of animals the farmer has.
ANSWER:
A farmer has sheep and cows in the ratio 8: 3
Number of cows = 180
Number of sheep = 480
We have to find the ratio of the number of sheep to the total number of animals the farmer has.
The ratio of the number of sheep to the total number of animals = 480 / 660
The ratio of the number of sheep to the total number of animals = 8:11
(iii) Find the ratio of the total number of animals with the farmer to the number of cows with him.
ANSWER:
A farmer has sheep and cows in the ratio 8: 3
Number of cows = 180
Number of sheep = 480
We have to find the ratio of the total number of animals with the farmer to the number of cows with him
The ratio of the total number of animals to the number of cows = 660 / 180
The ratio of the total number of animals to the number of cows = 11:3
9.) Are 3, 5, 15, 9 in proportion? If we change their order, can we think of proportional pairs?
ANSWER:
We have to check 3, 5, 15, 9 in proportion or not.
When 4 numbers are proportion then,
1st number x last number = 2nd number x 3rd number
3 x 9 = 5 x 15
27 = 75
Which are not equal.
3, 5, 15, 9 are not in proportion.
Now, when we change order such as 3, 5, 9, 15 and 5, 3, 15, 9 are in proportion.
10.) The temperature has dropped by 15 degree Celsius in the last 30 days. If the rate of temperature drop remains the same, how much more will the temperature drop in the next 10 days?
ANSWER:
Given,
The temperature has dropped by 15 degree Celsius in the last 30 days.
The rate of temperature drop remains the same.
We have to find how much more will the temperature drop in the next 10 days.
We 1st find temperature drop in 1 day.
Temperature drop in 1 day = 15 degree Celsius / 30 days.
Temperature drop in 1 day = 1/2 degree Celsius
Now,
Temperature drop in 10 day = 1/2 degree Celsius x 10
Temperature drop in 10 day = 5 degree Celsius
11.) Fill in the following blanks:
15 |
10 | ||
18 | 6 |
30 |
ANSWER:
We have to show the given fractions in simplest form.
15/18 when we divide by 3 we get,
15/18 = 5/6
Now,
When we multiply 2 with 5/6, we get,
2 x 5/6 = 10/12
15/18 = 5/6 = 10/12
Now,
When we multiply 2.5 with 10/12, we get,
2.5 x 10/12 = 25/30
15/18 = 5/6 = 10/12 = 25/30
12.) (i) 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 m) |
10 | 40 | ||||
Length of the hall (in m) | 25 | 50 |
|
ANSWER:
Ratio of breadth and length of a hall is 2: 5
Let, breadth and length of a hall are 2x and 5x respectively.
Now,
i) Length of a hall = 50 m
Length of a hall = 5x = 50
Length of a hall = x = 50/5 = 10
Breadth of a hall = 2x = 2 x 10 = 20m
ii)
Breadth of a hall = 40 m.
Breadth of a hall = 2x = 40
X = 40 / 2
X = 20
Length of a hall = 5x = 5 x 20 = 100 m
(ii) Find the ratio of length to breadth of your classroom.
ANSWER:
We have to find the ratio of length to breadth of your classroom.
Length of my classroom = 18 m.
Breadth of my classroom = 14 m.
The ratio of length to breadth of your classroom = 18: 14
The ratio of length to breadth of your classroom = 9:7
13.) Geetha earns Rs.12000 a month, out of which she saves Rs.3000. Find the ratio of her
Given,
Geetha earns Rs.12000 a month, out of which she saves Rs.3000.
We know,
Income – Expenditure = savings
12000 – Expenditure = 3000
Expenditure = Rs.9000
(i) Expenditure to savings
ANSWER:
Ratio of Expenditure to savings.
Expenditure = Rs.9000
Savings = Rs. 3000
Ratio of Expenditure to savings = Rs.9000: Rs. 3000
Ratio of Expenditure to savings = 3: 1
(ii) Savings to her income
ANSWER:
Ratio of Savings to her income
Savings = Rs. 3000
Income = Rs. 12000
Ratio of Savings to her income = Rs. 3000: Rs. 12000
Ratio of Savings to her income = 1:4
(iii) Expenditure to her income.
ANSWER:
Ratio of Expenditure to her income.
Expenditure = Rs.9000
Income = Rs.12000
Ratio of Expenditure to her income = Rs.9000: Rs.12000
Ratio of Expenditure to her income = 3:4
14.) There are 45 persons working in an office. The number of females is 25 and the remaining are males. Find the ratio of
Given,
There are 45 persons working in an office. The number of females is 25 and the remaining are males.
Number of males = 45 – 25
Number of males = 20
(i) The number of females to number of males
ANSWER:
Ratio of number of females to number of males.
Number of females = 25
Number of males = 20
Ratio of number of females to number of males = 25:20
Ratio of number of females to number of males = 5:4
(ii) The number of males to the number of females.
ANSWER:
Ratio of number of males to the number of females
Number of males = 20
Number of females = 25
Ratio of number of males to the number of females = 20:25
Ratio of number of males to the number of females = 4:5
15.) A bag of sweets contain yellow and green sweets. For every 2 yellow sweets, there are 6 green sweets. Complete this table based on the above information.
Yellow | 4 | 6 | |||
Green | 6 | 12 | 24 | ||
Total Sweets | 8 | 24 | 40 |
ANSWER:
Given,
For every 2 yellow sweets, there are 6 green sweets.
Now answer these questions.
(i) What is the ratio of green to yellow sweets?
ANSWER:
We have to find the ratio of green to yellow sweets
The ratio of green to yellow sweets = 2:6
The ratio of green to yellow sweets = 3:1
(ii) If you have 8 yellow sweets, how many green sweets will you have?
ANSWER:
We know,
The ratio of green to yellow sweets = 3:1
Green and yellow sweets are 3x and x.
Given, 8 yellow sweets
We have to find green sweets will you have.
x = 8
3x = 8 x 3 = 24 green sweets
(iii) If there are 32 sweets in the medium sized bag. How many will be yellow?
ANSWER:
Given, Total 32 sweets in the medium sized bag
We have to find how many will be yellow.
The ratio of green to yellow sweets = 3:1
Green and yellow sweets are 3x and x.
Total are 3x + x = 4x
32 sweets = 4x
X = 32/4
X = 8
Yellow sweets are 8
(iv) In the super fat size bag there are 40 sweets. How many will be green?
ANSWER:
Given, Total 40 sweets insuper fat size bag
We have to find how many will be green
The ratio of green to yellow sweets = 3:1
Green and yellow sweets are 3x and x.
Total are 3x + x = 4x
40 sweets = 4x
X = 40/4
X = 10
Yellow sweets are 10
Green sweets = 3x = 3 x 10 = 30 sweets
(v) In the sweet bowl if there are 16 yellow sweets. How many total sweets are in the bowl?
ANSWER:
There are 16 yellow sweets
We have to find total sweets are in the bowl
The ratio of green to yellow sweets = 3:1
Green and yellow sweets are 3x and x.
Given, x = 16 yellow sweets
Green sweets = 3x = 3 x 16 = 48 Green sweets
Total sweets =16 yellow sweets + 48 Green sweets
Total sweets = 64 sweets
16.) In a school survey it was found that for every 4 girls there were 5 boys.
Fill in the following table.
Girls | 4 | 8 | |||
Boys | 15 | 20 | |||
Total | 45 |
ANSWER:
Given,
In a school survey it was found that for every 4 girls there were 5 boys
Now answer these questions:
(i) What is the ratio of girls to boys?
ANSWER:
We have to find the ratio of girls to boys
Number of girls = 4
Number of boys = 5
The ratio of girls to boys = 4:5
(ii) In a class of 27 children, how many would be girls?
ANSWER:
The ratio of girls to boys = 4:5
Let, girls and boys are 4x and 5x respectively.
Total 27 children.
27 = 4x + 5x
27 = 9x
X = 27/9
X = 3
Girls are 4x = 4 x 3 = 12 girls
(iii) There are 54 children in a class. How many are boys?
ANSWER:
The ratio of girls to boys = 4:5
Let, girls and boys are 4x and 5x respectively.
Total 54 children.
54 = 4x + 5x
54 = 9x
X = 54/9
X = 6
Boys are 5x = 5 x 6 = 30 boys
(iv) If 20 girls join in a year. How many boys would join?
ANSWER:
The ratio of girls to boys = 4:5
Let, girls and boys are 4x and 5x respectively.
20 girls join in a year.
4x = 20
X = 20 / 4
X = 5
Boys would join = 5x = 5 x 5 = 25
25 boys would join in a year.
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