A company of 7300 soldiers formed of 4 battalions, so that 1/2 of the first = 2/3 of second = 3/4 of 3rd = 4/5 of the fourth are all composed of the same number. The difference between number of soldiers between the battalions with maximum and minimum number is?
Answers
Let the no of soldiers in the four battalions are A,B,C and D
Hence we know that
A+B+C+D = 7300
Now given,
A/2 = 2B/3 = 3C/4 = 4D/5 = k
=> A = 2k
B= 3k/2
C= 4k/3
D = 5k/4
putting these values in the eqn above we get
2k + 3k/2 + 4k/3 + 5k/4 = 7300
=> k(1/2 + 3/2 + 4/3 + 5/4) = 7300
=> k(73/12) = 7300
=> k = 1200
Hence putting the value of k in the above
A = 2k = 2400
B= 3k/2 = 1800
C= 4k/3 = 1600
D = 5k/4 = 1500
Therefore the maximum no of soldiers = A = 2400
minimum no of soldiers = D = 900
Hence their difference = 2400 - 1500 = 900
Therefore the difference between number of soldiers between the battalions with maximum and minimum number is 900.
Define x:
Let the 4th battalion has x number of soldiers
⇒ 4th battalion = x
Given 3/4 of 3rd battalion = 4/5 of the 4th battalion
⇒ 3rd battalion = (4/5 x) ÷ 3/4
⇒ 3rd battalion = 16/15 x
Given 2/3 of 2nd battalion = 3/4 of 3rd battalion
⇒ 2nd battalion = 3/4 (16/15 x) ÷ 2/3
⇒ 2nd battalion = 6/5 x
Given 1/2 of the 1st battalion = 2/3 of 2nd battalion
⇒ 1st battalion = 2/3 (6/5 x) ÷ 1/2
⇒ 1st battalion = 8/5 x
Solve x:
There are 7300 soldiers
x + 16/15 x + 6/5 x + 8/5 x = 7300
73/15 x = 7300
x = 7300 ÷ 73/15
x = 1500
Find the number of soldiers in each battalion:
1st battalion = x = 1500
2nd battalion = 16/15 x = 16/15 (1500) = 1600
3rd battalion = 6/5 x = 6/5 (1500) = 1800
4th battalion = 8/5 x = 8/5 (1500) = 2400
Find the difference between the maximum and minimum:
Max = 2400
Min = 1500
Difference = 2400 - 1500 = 900
Answer: The difference between the maximum and minimum is 900 soldiers.