Question

20. For 71th republic day Parade on 26/01/2021 in Delhi, Captain RS Meel is planning for

parade of following two groups: (1) First group of Army contingent of 624 members

behind an army band of 32 members. (2) Second group of CRPF troops with 468

soldiers behind the 228 members of bikers. These two groups are to march in the same

number of columns. This sequence of soldiers is followed by different states of Jhanki

which are showing the culture of the respective states.





(i) What is the maximum number of columns in which the army troop can march?

a) 8 b) 16 c) 4 d) 32

(ii) What is the maximum number of columns in which the CRPF troop can march?

a) 4 b) 8 c) 12 d) 16

(iii) What is the maximum number of columns in which total army troop and CRPF troop

together can march past?

a) 2 b) 4 c) 6 d) 8​

Answer 1

Answer:

1.a)16

2.c)12

3.d)8

4.a)4 solders and 4 bikers

5d)12 solders and 6 bikers

Answer 2

Answer:

The correct answer to the problems are found to be as follows:

(i) - option (b) 16 columns

(ii) - option (c) 12 columns

(iii) - option (b) 4 columns

Step-by-step explanation:

The maximum number of columns in which the troops with different number of participants can organise themselves in a parade is found by finding the Greatest common factor (HCF) of the two numbers.

(i) Now, for finding the maximum number of columns in which the army troops can march, we find the HCF of 624 and 32:

By factorization:

624 = 2 x 2 x 2 x 2 x 3 x 13

32  =  2 x 2 x 2 x 2 x 2

HCF = 2 x 2 x 2 x 2 = 16

Thus, the number of columns in which the army troop can move is 16.

(ii) Similarly, for finding the maximum number of columns in which the CRPF troops can march, we find the HCF of 468 and 228:

By factorization:

468 = 2 x 2 x 3 x 3 x 13

228 = 2 x 2 x 3 x 19

HCF = 2 x 2 x 3 = 12

Thus, the number of columns in which the CRPF troop can move is 12.

(iii) Now, for finding the number of columns in which the total troops (army as well as CRPF) can march, we can find the HCF of 12 and 16,

By factorization:

12 = 2 x 2 x 2 x 2

16 =  2 x 2 x 3

HCF = 2 x 2 = 4

Thus, the number of columns in which the total troops can move is 4.

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