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.

**–: **Unitary Method Class 6 RS Aggarwal Exe-9A Goyal Brothers ICSE Maths Solutions** :–**

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