Selina Solutions Concise Mathematics Class 6 Chapter 13 Unitary Method Exercise 13(A) provides a clear cut picture of the concepts, which are essential from the exam perspective. The solutions are formulated by expert teachers in an interactive way, helping students in solving the complex questions, with ease. Practising these solutions on a daily basis improves students’ academic performance. To increase conceptual knowledge among students, Selina Solutions Concise Mathematics Class 6 Chapter 13 Unitary Method Exercise 13(A), PDF links are given here for free download
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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
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