Q. The Republic Day parade, first held in 1950, has been a yearly ritual since. The parade marches from the Rashtrapati Bhawan along the Rajpath in New Delhi. Several regiments of the army, navy, and air force, along with their bands, march to India Gate. The parade is presided over by the President of India, who is the Commander-in-Chief of the Indian Armed Forces. As he unfurls the tricolour, the national anthem is played.The regiments of the Armed Forces then start their march past. Prestigious awards like Kirti Chakra, Ashok Chakra, Paramvir Chakra and Vir Chakra are given out by the President. Nine to twelve different regiments of the Indian Army, in addition to the Navy and Air Force march toward India Gate along with their bands. Contingents of paramilitary forces and other civil forces also participate in the parade. On 71th republic day parade, captain RS Meel is planing for parade of following two group:
(a) First group of Army troops of 624 members behind an army band of 32 members.
(b) 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 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
(iv) What should be subtracted with the numbers of CRPF soldiers and the number of bikers so that their maximum number of column is equal to the maximum number of column of army troop?
(a) 4 Soldiers and 4 Bikers
(b) 4 Soldiers and 2 Bikers
(c) 2 Soldiers and 4 Bikers
(d) 2 Soldiers and 2 Bikers
(v) What should be added with the numbers of CRPF soldiers and the number of bikers so that their maximum number of column is equal to the maximum number of column of army troop?
(a) 4 Soldiers and 4 Bikers
(b) 12 Soldiers and 12 Bikers
(c) 6 Soldiers and 6 Bikers
(d) 12 Soldiers and 6 Bikers
(a) First group of Army troops of 624 members behind an army band of 32 members.
(b) 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 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
(iv) What should be subtracted with the numbers of CRPF soldiers and the number of bikers so that their maximum number of column is equal to the maximum number of column of army troop?
(a) 4 Soldiers and 4 Bikers
(b) 4 Soldiers and 2 Bikers
(c) 2 Soldiers and 4 Bikers
(d) 2 Soldiers and 2 Bikers
(v) What should be added with the numbers of CRPF soldiers and the number of bikers so that their maximum number of column is equal to the maximum number of column of army troop?
(a) 4 Soldiers and 4 Bikers
(b) 12 Soldiers and 12 Bikers
(c) 6 Soldiers and 6 Bikers
(d) 12 Soldiers and 6 Bikers
Answers & Comments
(i) What is the maximum number of columns in which the army troop can march?
To determine the maximum number of columns in which the army troop can march, we need to find the greatest common divisor (GCD) of the number of soldiers and the number of band members.
Number of soldiers = 624
Number of band members = 32
GCD(624, 32) = 8
So, the maximum number of columns in which the army troop can march is 8.
Answer: (a) 8
(ii) What is the maximum number of columns in which the CRPF troop can march?
Similar to the previous question, we need to find the GCD of the number of CRPF soldiers and the number of bikers.
Number of CRPF soldiers = 468
Number of bikers = 228
GCD(468, 228) = 12
So, the maximum number of columns in which the CRPF troop can march is 12.
Answer: (c) 12
(iii) What is the maximum number of columns in which the total army troop and CRPF troop together can march past?
To find the maximum number of columns in which both troops can march together, we need to find the GCD of the total number of soldiers in both troops.
Total number of soldiers = 624 (army) + 468 (CRPF) = 1092
GCD(1092, 32) = 4
So, the maximum number of columns in which the total army troop and CRPF troop together can march past is 4.
Answer: (b) 4
(iv) What should be subtracted with the numbers of CRPF soldiers and the number of bikers so that their maximum number of columns is equal to the maximum number of columns of the army troop?
We already know that the maximum number of columns for the army troop is 8. To make the CRPF troop match this, we need to subtract the difference.
Difference = Maximum columns of army troop - Maximum columns of CRPF troop
Difference = 8 - 12
Difference = -4
Since we can't have a negative number of soldiers or bikers, we cannot achieve the same number of columns for the CRPF troop as the army troop by subtracting.
(v) What should be added with the numbers of CRPF soldiers and the number of bikers so that their maximum number of columns is equal to the maximum number of columns of the army troop?
To make the CRPF troop match the maximum columns of the army troop (8), we need to add the difference.
Difference = Maximum columns of army troop - Maximum columns of CRPF troop
Difference = 8 - 12
Difference = -4
To make it positive and match the army troop's 8 columns, we need to add 4.
So, the answer is:
Answer: (a) 4 Soldiers and 4 Bikers