If (a – b + c) : (b – c + 2d) : (2a + c – d) = 2 : 3 : 5, then find (3a + 3c – 2d) : d.
Shortcut:-
Given: a-b+c = 2k b-c+2d = 3k 2a+c-d = 5k
now divide all the equation on both side by "d" and say
a/d = x b/d =y c/d =z k/d = w
Then the given equation changes to ,
x-y+z = 2w ------------------ (1)
y-z+2 = 3w -------------------(2)
2x+z-1 = 5w -------------------(3)
We need to find out (3a+3c-2d):d which is equal to 3 (a/d) + 3(c/d) - 2 = 3x+3z-2.
i.e we need to find 3(x+z)-2 .
NOW add equation 1 and 2, we get x = 5w-2.
Put this value of x in equation 3 , we get z= -5w+5.
Put these value of x and z in 3x+3z-2.
we get , 3( x+z) - 2 = 3( 5w - 2 - 5w + 5 ) - 2 = 3(3) -2 = 9-2 = 7 is the answer.
Now since the question is in ration form we can write it as 7: 1.
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given that:
(a – b + c) : (b – c + 2d) : (2a + c – d) = 2 : 3 : 5, then find (3a + 3c – 2d) : d
a-b+c = 2k .............(1)
b-c+2d = 3k ...........(2)
2a+c-d = 5k ...........(3)
adding (1) and (2)
a+2d = 5k
a=5k-2d .........(4)
using (3)
c = 5k+d-2a
c = 5k+d-2(5k-2d)
c = 5d -5k .......(5)
using (2)
b-c+2d = 3k
3a+3c-2d =3(5k-2d)+3(5k-5d)-2d
3a+3c-2d = 15k -6d +15k-15d-2d
3a+3c-2d = 30k-23d =d
30k =24d
5k = 4d ...... ....(6)
using ....(4), (5) and (6)
a = 2d, and c = d
therefore
3a+3c-2d =6d +3d -2d =7d
Hence ratio is 7:1