SOLUTION: Rs 5625 is divided among A,B and C so that A may receive 1/2 as much as B and C together receive and B receives 1/4 of what A and C together receive.The share of A is more than tha

Algebra ->  Equations -> SOLUTION: Rs 5625 is divided among A,B and C so that A may receive 1/2 as much as B and C together receive and B receives 1/4 of what A and C together receive.The share of A is more than tha      Log On


   

Question 460139: Rs 5625 is divided among A,B and C so that A may receive 1/2 as much as B and C together receive and B receives 1/4 of what A and C together receive.The share of A is more than that of B by?
Options are
a)rs 750
b)Rs 1500
c)Rs 775
d)Rs 1600
Answer is rs 750
Please explain the method
Thanks!
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
2a=b+c
4b=a+c
a+b+c=5625
..
2a-b-c= 0-------------- 1
-a+4b-c =0--------------2
a+b+c=5625--------------3

consider equation 1 &2 Eliminate b
Multiply 1 by 4
Multiply 2 by 1
we get
8a-4b-4 c=0
-a+4b-c=0
Add the two
7a-5c=0 ------------- 4
consider equation 2 & 3 Eliminate b
Multiply 2 by 1
Multiply 3 by -4
we get
- a + 4 b + - c = 0
-4 a -4 b -4 c = -22500
Add the two
-5a-5c= -22500 -------------5 5
Consider (4) & (5) Eliminate a
Multiply 4 by 5
Multiply (5) by 7
we get
35 a -25 c = 0
-35 a -35 c = -157500
Add the two
-60 c = -157500
/ -60
c = 2625

Plug the value of c in 5
-5 a -13125 = -22500
-5 a = -9375
a = 1875
plug value of a & c in 1
3750 - b + -2625 = 0
-1 b = -3750 + 2625 + 0
b= 1125
a-b=750