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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.
Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.
Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.
Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.
Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.
Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.
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