Class 10 Case based problem of Chapter 1 Real Number 1

Case based:1

     A seminar is being conducted by an educational organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.

 Class 10 Case based problem of Chapter 1 Real Number 1

(A)  In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number of participants that can be accommodated in each room are:

(a) 14                      (b) 12

(c) 16                       (d) 18

(B) What is the minimum number of rooms required during the event ?

(C) The LCM of 60, 84 and 108 is :

(a) 3780                (b) 3680

(c) 4780                 (d) 4680

(D)  The product of HCF and LCM of 60, 84 and 108 is :

(a) 55360               (c) 35360

(c) 45500                (d) 45360

(E) Express 108 as a product of its primes:

Solution:

(A) Answer is (b) 12

Explanation:-

60 =  2 × 2 × 3 × 5

84 = 2 × 2×3 × 7

108 = 2 × 2 × 3 × 3

HCF(60, 84, 108) = 2 × 2 × 3 = 12

Hence the maximum number of participants that can be accommodated in a room is 12.

(B) Number of rooms required by participants of subject hindi

=\frac{\text{Total number of participants of Hindi }}{\text{ Maximum number of participants in each room }}

=\frac{60}{12}=5

Similarly

Number of rooms required by participants of english

=\frac{84}{12}=7

Number of rooms required by participants of Mathematics

=\frac{108}{12}=9

\therefore Minimum number of rooms required

= 5 + 7+ 9=21

(C) Answer is (a) 3780

Explanation:-

60 =  2 × 2 × 3 × 5

84 = 2 × 2×3 × 7

108 = 2 × 2 × 3 × 3

\therefore  LCM(60, 84, 108) = 2 × 2× 3 × 3 × 3 × 5 × 7

= 3780

(D) Answer is (b) 45360

Explanation :-

From parts (A) and (C)

HCF(60, 84, 108) = 12

LCM(60, 84, 108) = 3780

∴  HCF × LCM  = 12 × 3780

= 45360

(E) 108 = 2 × 2 × 3 × 3 × 3

= 2^2 \times 3^3

Other question:-

Class 10 Case based problem of Chapter 1 Real Number 1

Class 10 Case based problem of Chapter 1 Real Number 2

Question:-Ruhi invested a certain amount of money in two schemes

Question:- rahul-had-some-bananas-and-he-divided-them-into-two-lots

gmath.in

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