Unitary Method Class 6 RS Aggarwal Exe-9A Goyal Brothers ICSE Maths Solutions Ch-9. In this article you will learn about Direct Variation . Visit official Website CISCE for detail information about ICSE Board Class-6 Mathematics.
Unitary Method Class 6 RS Aggarwal Exe-9A Goyal Brothers ICSE Maths Solutions Ch-9
| Board | ICSE |
| Subject | Maths |
| Class | 6th |
| Ch-9 | Unitary Method |
| Writer | RS Aggrawal |
| Book Name | Foundation |
| Topics | Solution of Exe-9A |
| Academic Session | 2024 – 2025 |
What is Unitary Method – Direct Variation?
The unitary method is a basic concept to find the value of a single unit and then using that value to find the value of multiple units
Direct Variation: The value of multiple units increases with an increase in the number of units and voice versa.
How to Solve Direct Variation of Unitary Method Questions/Problems
- First we find the value of unit quantity by dividing the given value by the given quantity.
- Thus we obtain the value of unit quantity.
- We then multiply the required quantity with the obtained value.
- Therefore we get the value of the required quantity
Exercise- 9A
(Unitary Method Class 6 RS Aggarwal Goyal Brothers ICSE Maths Solutions Ch-9)
Que-1: The cost of 11 pens in Rs253. Find (i) the cost of one pen (ii) the cost of 24 pens
Sol: (i) The cost of 11 pens = ₹ 253
the cost of 1 pen = 253/11
= ₹ 23
(ii) Cost of 24 pens
= 24 × 23
= Rs552.
Que-2: 14 tins contain 210 litres of oil. How much oil is contained in (i) 1 tin, (ii) 18 tins ?
Sol: (i) 14 tins contain = 210 litres
1 tin contain = 210/14
= 15 litres.
(ii) 18 tins contain
= 18 × 15
= 270 litres.
Que-3: On 26 litres of diesel, a car runs 192 km. How many kilometres will it run on (i) 1 litre, (ii) 25 litres ?
Sol: (i) For 1 litre diesel,
16 litres = 192 km
1 litre = x
By cross multiplication we get,
16 × x = 192
16x = 192
x = 192/16 = 12 km
(ii) For 25 litre diesel,
16 litres = 192 km
25 litres = X
By cross multiplication we get,
16 × X = 192 × 25
16x = 4800
X = 4800/16 = 60 km.
Que-4: If 8kg rice costs Rs620, what will be the cost of 18kg of rice ?
Sol: 8kg = ₹620
18kg?
18/8 = 2.25
₹620 x 2.25 = ₹1,395
Que-5: If the cost of 13m of cloth Rs1664, what will be the cost of 15m of the same cloth ?
Sol: The price of 13m of cloth= 1664
Price of 1m of cloth= 1664/13
= 128
Price of 15m of cloth= 128×15
=1920
Que-6: If 15 tins of the same size contain 235kg of oil, how much oil will be there in 12 such tins ?
Sol: 15 tins / 235 kg = 12 tins / x kg
To solve for x, you can cross multiply and divide:
15 tins * x kg = 235 kg * 12 tins
x kg = 235 kg * 12 tins / 15 tins
x kg = 188 kg
Que-7: If 6m of a uniform iron rod weighs 21kg, what will be the weight of 20m of the same rod ?
Sol: 6m of a uniform iron rod = 21kg
20m?
6m = 21kg
20m = ___kg
20÷6 = 10/3
=> this means 6 x 10/3 is 20
so we will have to multiply 10/3 on the right-hand side as well
21 x 10/3 = 70
Que-8: The weight of 63 books of the same size is 28kg. How many such books will weigh 60kg ?
Sol: Given ,
63 books weigh 28 kg
Then, 1 book weight is 28/63 → (1)
If one book weight is 28/63 then the weight of X books is 60 kg
1 → 28/63
X → 60 kg
Therefore, X = 60×(63/28)
= 135 books
Que-9: If the cost of 25 bananas is Rs95, how many bananas can be bought for Rs152 ?
Sol: Cost of 25 bananas = 95
1 banana = 95/25
= 3.8
total amount with us = 152
bananas = 152/3.8
= 40 bananas
Que-10: 15 boxes of the same size contain 1080 pens. How many such boxes will be needed for 1800 pens ?
Sol: no. of pens in one box = 1080/15 = 72.
no. of boxes needed for 1800 pens = 1800/72 = 25
∴no. of boxes needed for 1800 pens is 25.
Que-11: A car travels 204 km in 9 hours. How long will it take to travel 340 km ?
Sol: Let the time be X
204/9 = 340/X
204×X = 340×9
204X = 3060
X = 3060/204
X = 15 hours
Que-12: A bus consumes 12.5 litres of diesel in covering a distance of 65 km. How much diesel will it consume in covering 416 km ?
Sol: 12.5 litres in 65 km
1 litre = 65/12.5
= 5.2
In covering 416 km
= 416 ÷ 5.2
= 80 litres.
Que-13: 44 metres of cloth is required to make 20 shirts. How much cloth will be required to make 35 such shirts ?
Sol: 20 shirts can be made = 44 m of cloth
1 shirt can be made = 44/20 m of cloth
35 shirts can be made = 44/20 × 35
= 11×7
= 77
Que-14: 18 bags of rice having equal weights weigh 297 kg. How much will 22 such bags weigh ?
Sol: 18 bags weight 297kg.
Weight of one bag =
297 ÷ 18
= 16.5 kg
Weight of 22 bags =
= 16.5 × 22
= 363 kg.
Que-15: If a man walks 14 km in 5 hours, how long would he take to walk 22.4 km ?
Sol: In 14km = 5 hours
In 1 km = 5/14
= 0.357
In 22.4 km = 22.4×0.357
= 8 hours.
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