Question

Solves the following

1. The length, breath and height of a room are 825 cm, 675 cm and 450 cm

respectively. Find the longest tape which can measure the three dimensions of the

room exactly.

2. What is the HCF of two consecutive?

(a) Numbers? (b) Even numbers? (c) Odd numbers?

3. A vendor supplies 32 L of milk to a hotel in the morning and 68 L of milk in the

evening if the milk cost Rs.45 per litre how much money is due to the vendor per

day?

4. Estimate the following products using general rule

(A) 578 * 161

(B) 5281* 3491

(C) 1291* 592​

Answer 1

We need to find H.C.F of 825, 675 and 450 which would be equal to the longest tape which can measure the three dimensions of the room exactly.

Let's find the prime factors of 825, 675 and 450.

825=3×5×5×11

 

675=3×3×3×5×5

 

 

450=2×3×3×5×5

 

 

3, 5 and 5 are the common prime factors.

 

Therefore. H.C.F =3×5×5=75

 

Therefore, 75 cm is the longest tape which can measure the three dimensions of the room exactly

2. 2 is the H.C.F of two consecutive even numbers. ... 2 is the H.C.F for numbers 10 and 12 because 2 is the only common prime factor for both 10 and 12. Answer (c) 1 is the H.CF of two consecutive odd numbers.

3.quantity of milk supplied in da morning=32 liters

quantity of milk supplied in da evening = 68 litres

⇒ total milk per litre = (32+68) litre

⇒cost of milk per litre = rs 15

∴ total cosr per day = 15*(32+68)  

                              =15*100

                               = rs 1500

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Answer 2

Answer:

1.Length=825cm =3×5×5×11

Breadth=675cm =3×3×3×5×5

Height=450cm =2×3×3×5×5

Longest tape=HCF of 825,675 and 450=3×5×5=75cm

Therefore, the longest tape is 75cm.

2.(a) 1 is the HCF of two consecutive numbers

(b)2 is the HCF of two consecutive even numbers

(c)1 is the HCF of two consecutive odd numbers

3.Quantity of milk supplied in the morning =32

Quantity of milk supplied in the evening =68

Total of milk per litre =(32+68)

Cost of milk per litre =Rs. 15

Total cost per day=15×(32+68)

=15×100=Rs. 1500.

(a) 578 x 161 578 round off to 600 161 round off to 200 The estimated product = 600 x 200 = 1,20,000

(b)5281 x 3491 5281 round of to 5,000 3491 round off to 3,500 The estimated product = 5,000 x 3,500 = 1,75,00,000

(c) 1291 x 592 1291 round off to 1300 592 round off to 600 The estimated product = 1300 x 600 = 7,80,000

All the answers are here.

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