Selina Solutions Concise Mathematics Class 6 Chapter 13 Unitary Method gives a clear idea of the concepts covered, with examples, which help students for better understanding. The various examples present in the textbook, before each exercise, help them to obtain a better hold on the subject. Constant practice of exercise wise problems, help students in scoring high marks in the final examination. For more conceptual knowledge, students can use Selina Solutions Concise Mathematics Class 6 Chapter 13 Unitary Method PDF, from the links given below
Chapter 13 explains the technique of solving problems by first finding the value of a single unit and then multiplying this single unit value for the required number of units. Solutions prepared by experts in a descriptive manner help in boosting exam preparation among students
Selina Solutions Concise Mathematics Class 6 Chapter 13: Unitary Method Download PDF
Exercises of Selina Solutions Concise Mathematics Class 6 Chapter 13: Unitary Method
Access Selina Solutions Concise Mathematics Class 6 Chapter 13: Unitary Method
Exercise 13(A)
1. The price of 25 identical articles is Rs 1,750. Find the price of:
(i) one article
(ii) 13 articles
Solution:
(i) one article
Given
The price of 25 identical articles = 1,750
Hence, the price of one article can be calculated as follows:
Price of one article = 1750 / 25
= Rs 70
∴ The price of one article is Rs 70
(ii) 13 articles
Given
Price of 25 identical articles = 1, 750
Hence, the price of thirteen articles can be calculated as follows:
Price of one article = 1750 / 25
= Rs 70
Price of thirteen articles = 13 × 70
= Rs 910
∴ The price of thirteen articles is Rs 910
2. A motorbike travels 330 km in 5 litres of petrol. How much distance will it cover in:
(i) one litre of petrol?
(ii) 2.5 litres of petrol?
Solution:
(i) one litre of petrol
Given
A motorbike travels 330 km in 5 litres of petrol
Hence, distance covered in one litre of petrol can be calculated as follows:
Distance covered by bike in one litre of petrol = 330 / 5
= 66 km
∴ The bike covers 66 km of distance in one litre of petrol
(ii) 2.5 litres of petrol
Given
A motorbike travels 330 km in 5 litres of petrol
Hence, distance covered in 2.5 litres of petrol can be calculated as follows:
Distance covered by bike in 2.5 litres of petrol = 2.5 × 66
= 165 km
∴ The bike covers 165 km of distance in 2.5 litres of petrol
3. If the cost of a dozen soaps is Rs 460.80, what will the cost of:
(i) each soap?
(ii) 15 soaps?
(iii) 3 dozen soaps?
Solution:
(i) each soap
Given
Cost of one dozen soaps = Rs 460.80
We know that,
12 soaps = one dozen
Hence the price of one soap can be calculated as follows:
Price of one soap = 460.80 / 12
= Rs 38.4
∴ The price of one soap is Rs 38.4
(ii) 15 soaps
Given
Cost of one dozen soaps = Rs 460.80
We know that,
12 soaps = one dozen
Hence the price of fifteen soaps can be calculated as follows:
Price of one soap = 460.80 / 12
= Rs 38.4
Price of fifteen soaps = 15 × 38.4
= Rs 576
∴ The price of fifteen soaps is Rs 576
(iii) 3 dozen soaps
Given
Cost of one dozen soaps = Rs 460.80
We know that,
12 soaps = one dozen
3 dozen contains = (12 × 3 = 36)
3 dozen = 36 soaps
Hence the price of 3 dozen soaps can be calculated as follows:
Price of one soap = 460.80 / 12
= Rs 38.4
Price of 3 dozen soaps = 36 × 38.4
= Rs 1382.4
∴ The price of three dozen soaps is Rs 1382.4
4. The cost of 35 envelops is Rs 105. How many envelops can be bought for Rs 90?
Solution:
Given
Cost of 35 envelops = Rs 105
Hence the number of envelops can be bought for Rs 90 can be calculated as below
Number of envelops bought in Rs 105 = 35
Envelops bought in Rs 1 = 35 / 105
Number of envelops bought in Rs 90 = 35 / 105 × 90
= 30
∴ 30 envelops can be bought in Rs 90
5. If the cost of 8 cans of juice is Rs 280, then what will be the cost of 6 cans of juice?
Solution:
Given
Cost of 8 cans of juice = Rs 280
Hence, cost of 6 cans of juice can be calculated as below
Cost of 1 can juice = 280 / 8
= Rs 35
Cost of 6 cans of juice = 6 × 35
= Rs 210
∴ The cost of 6 cans of juice will be Rs 210
6. For Rs 378, 9 cans of juice can be bought, then how many cans of juice can be bought for Rs 504?
Solution:
Given
Amount in which 9 cans of juice can be bought = Rs 378
Number of juice cans bought in Rs 378 = 9 cans
Juice can bought in Rs 1 = 9 / 378
Number of juice cans bought in Rs 504 = 9 / 378 × 504
= 12
∴ 12 cans of juice can be bought in Rs 504
7. A motorbike travels 425 km in 5hours. How much distance will be covered by it in 3.2 hours?
Solution:
Given
Distance covered by motorbike in 5 hours = 425 km
Distance covered by bike in 3.2 hours can be calculated as below
Distance covered in 1 hour = 425 / 5
= 85 km
Distance covered by bike in 3.2 hours = 85 × 3.2
= 272 km
∴ Distance covered by bike in 3.2 hours is 272 km
8. If the cost of a dozen identical articles is Rs 672, what will be the cost of 18 such articles?
Solution:
Given
Cost of a dozen identical articles = Rs 672
We know that,
Number of articles in one dozen = 12
Hence the price of 18 articles can be calculated as below
Price of one article = 672 / 12
= Rs 56
Price of eighteen articles = 18 × 56
= Rs 1008
∴ Cost of 18 articles will be Rs 1008
9. A car covers a distance of 180 km in 5 hours.
(i) How much distance will the car cover in 3 hours with the same speed?
(ii) How much time will the car take to cover 54 km with the same speed?
Solution:
(i)
Given
Distance covered by car in 5 hours = 180 km
Hence distance covered by car in 3 hours can be calculated as below
Distance covered by car in 1 hour = 180 / 5
= 36 km
Distance covered by car in 3 hours = 36 × 3
= 108 km
∴ Distance covered by car in 3 hours with the same speed will be 108 km
(ii)
Given
Distance covered by car in 5 hours = 180 km
Hence time taken by the car to cover 54 km distance can be calculated as below
Time taken by the car to cover 180 km distance = 5 hours
Time taken by the car to cover 1 km distance = 5 / 180 hour
Time taken to cover 54 km distance by car = 5 / 180 × 54
= 1.5 hours
∴ Time taken to cover 54 km distance by the car is 1.5 hours
10. If it has rained 276 cm in the last 3 days, how many cm of rain will fall in one week (7 days)?
Assume that the rain continues to fall at the same rate.
Solution:
Given
Cm of rainfall in 3 days = 276 cm
Hence, rainfall in one week can be calculated as below
Rainfall in one day = 276 / 3
= 92 cm
Rainfall in 7 days = 92 × 7
= 644 cm
Therefore, 644 cm of rain will fall in one week.
11. Cost of 10 kg of wheat is Rs 180
(i) What is the cost of 18 kg of wheat?
(ii) What quantity of wheat can be purchased in Rs 432?
Solution:
(i) Given
Cost of 10 kg of wheat = Rs 180
Hence the cost of 18 kg wheat can be calculated as below
Cost of 1 kg wheat = 180 / 10
= Rs 18
Cost of 18 kg wheat = 18 × 18
= Rs 324
∴ The cost of 18 kg wheat is Rs 324
(ii) Given
Cost of 10 kg wheat = Rs 180
Hence the quantity of wheat can be purchased in Rs 432 can be calculated as below
Wheat purchased in Rs 180 = 10 kg
Wheat purchased in Rs 1 = 10 / 180
Wheat purchased in Rs 432 = 10 / 180 × 432
= 24 kg
∴ 24 kg wheat can be purchased in Rs 432
12. Rohit buys 10 pens for Rs 150 and Manoj buys 14 pens for Rs 168. Who got the pens cheaper?
Solution:
Given
Amount in which Rohit buys 10 pens = Rs 150
Amount in which Manoj buys 14 pens = Rs 168
Cost of 1 pen of Rohit = 150 / 10
= Rs 15
Cost of 1pen of Manoj = 168 / 14
= Rs 12
∴ The cost of Manoj pen is cheaper than Rohit. Hence Manoj purchase the cheaper pen
13. A tree 24 m high casts a shadow of 15 m. At the same time, the length of the shadow casted by some other tree is 6 m. Find the height of the tree.
Solution:
Given
Tree of 24 height cast a shadow of 15 m
Hence, the length of shadow casted by other tree of 6 m can be calculated as below
Height of tree which casts shadow of 15 m = 24 m
Height of tree which casts shadow of 1 m = 24 / 15 m
Height of tree which casts the shadow of 6 m = 24 / 15 × 6 m
= 9.6 m
∴ Length of the tree which casts the shadow of 6 m is 9.6 m
14. A loaded truck travels 18 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours?
Solution:
Given
A loaded truck travels 18 km in 25 minutes
We know
1 hour = 60 min
5 hours = 5 × 60
= 300 min
Distance covered by the truck in 25 min = 18 km
Distance covered by the truck in 1 min = 18 / 25 km
Distance covered by the truck in 300 min = 18 / 25 × 300 km
= 216 km
∴ Distance travelled by the truck in 5 hours is 216 km
Exercise 13(B)
1. Weight of 15 books is 6 kg. What is the weight of 45 such books?
Solution:
Given
Weight of 15 books = 6 kg
Hence weight of 45 books can be calculated as below
Weight of one book = 6 / 15 kg
Weight of 45 books = 6 / 15 × 45
= 18 kg
∴ The weight of 45 books is 18 kg
2. A made 84 runs in 6 overs and B made 126 runs in 7 overs. Who made more runs per over?
Solution:
Given
Runs scored by A in 6 overs = 84 runs
Runs scored by B in 7 overs = 126 runs
Hence runs scored by A and B per over can be calculated as below
Runs scored by A in one over = 84 / 6
= 14 runs
Runs scored by B in one over = 126 / 7
= 18 runs
∴ Runs scored by B is more than A per over
3. Geeta types 108 words in 6 minutes. How many words would she type in half an hour?
Solution:
Given
Geeta types 108 words in 6 minutes
We know
1 hour = 60 minutes
Half an hour = 30 minutes
Hence number of words typed by Geeta in 30 minutes can be calculated as below
Words typed by Geeta in 1 minute = 108 / 6
= 18 words
Words typed by Geeta in 30 minutes = 18 × 30
= 540 words
∴ Geeta type 540 words in 30 minutes
4. The temperature dropped 18 degree Celsius in the last 24 days. If the rate of temperature drop remains the same, how many degrees will the temperature drop in the next 18 days?
Solution:
Given
Temperature dropped 18 degree Celsius in 24 days
Hence temperature drop in next 18 days can be calculated as below
Temperature drop in 24 days = 180 C
Temperature drop in 1 day = 180 C / 24
Temperature drop in 18 days = 18 × 180 C / 24
= 13.50 C
∴ Temperature drop in next 18 days will be 13.50 C
5. Mr. Chopra pays Rs 12,000 as rent for 3 months. How much does he has to pay for a year if the rent per month remains same?
Solution:
Given
Rent paid by Chopra for 3 months = Rs 12,000
Hence rent of 12 months can be calculated as below
Rent of 1 month = 12000 / 3
= Rs 4000
Rent of 12 months = 12 × 4000
= Rs 48000
∴ The rent of 12 months is Rs 48000
6. A truck requires 108 litres of diesel for covering a distance of 1188 km. How much diesel will be required by the truck to cover a distance of 3300 km?
Solution:
Given
A truck requires 108 litres of diesel for covering a distance of 1188 km
Diesel required to cover 1188 km distance by a truck = 108 litres
Diesel required to cover 1 km distance by a truck = 108 / 1188 litres
Diesel required to cover 3300 km distance = 108 / 1188 × 3300
= 300 litres
∴ A truck requires 300 litres of diesel to cover a distance of 3300 km
7. If a deposit of Rs 2,000 earns an interest of Rs 500 in 3 years, how much interest would a deposit of Rs 36,000 earn in 3 years with the same rate of simple interest?
Solution:
Given
Interest earned on deposit of Rs 2000 for 3 years = Rs 500
Hence interest earned on deposit of Rs 36000 for 3 years can be calculated as below
Interest earned on deposit of Rs 2000 for 3 years = Rs 500
Interest earned on deposit of Rs 1 for 3 years = Rs 500 / 2000
Interest earned on deposit of Rs 36000 for 3 years = Rs 36000 × 500 / 2000
= Rs 9000
∴ Amount earned on deposit of Rs 36000 in 3 years is Rs 9000
8. If John walks 250 steps to cover a distance of 200 metres, find the distance covered by him in 350 steps.
Solution:
Given
Distance covered by John to walk 250 steps = 200 metres
Hence distance covered by John to walk 350 steps can be calculated as below
Distance covered in one step = 200 / 250
Distance covered in 350 steps = 350 × 200 / 250 m
= 280 m
∴ Distance covered by John to walk 350 steps is 280 m
9.25 metres of cloth costs Rs 1,012.50
(i) What will be the cost of 20 metres of cloth of the same type?
(ii) How many metres of the same kind can be bought for Rs 1,620?
Solution:
(i) Given
Cost of 25 metre cloth = Rs 1012.50
Hence the cost of 20 metre cloth can be calculated as below
Cost of 1 metre cloth = Rs 1012.50 / 25
Cost of 20 metre cloth = Rs 20 × 1012.50 / 25
= Rs 810
∴ Cost of 20 metre cloth is Rs 810
(ii) Given
Cost of 25 metre cloth = Rs 1012.50
Hence cloth purchased in Rs 1620 can be calculated as below
Cloth purchased by Rs 1012.50 = 25 metre
Cloth purchased by Rs 1 = 25 / 1012.50 m
Cloth purchased by Rs 1620 = 1620 × 25 / 1012.50 m
= 40 m
∴ 40 metre cloth can be purchased in Rs 1620
10. In a particular week, a man works for 48 hours and earns Rs 4, 320. But in the next week he worked 6 hours less, how much has he earned in this week?
Solution:
Given
Amount earned by a man for working 48 hours = Rs 4320
Work done by him for 6 hours less than last week = 48 – 6
= 42 hours
Hence money earned by a man in 42 hours can be calculated as below
Money earned in one hour = 4320 / 48
Money earned in 42 hours = 42 × 4320 / 48
= Rs 3780
∴ In 42 hours a man earns Rs 3780
Comments