CA Foundation Exam > CA Foundation Questions > If A = B/2 = C/5, then A : B : C isa)3 : 5 : ...
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If A = B/2 = C/5, then A : B : C is
- a)3 : 5 : 2
- b)2 : 5 : 3
- c)1 : 2 : 5
- d)none of these
Correct answer is 'C'. Can you explain this answer?
Verified Answer
If A = B/2 = C/5, then A : B : C isa)3 : 5 : 2b)2 : 5 : 3c)1 : 2 : 5d)...
I think you take all in respect to A and cut it out
∴ a= a
b = 2a
c= 5a
a:b:c = 1:2:5
∴ a= a
b = 2a
c= 5a
a:b:c = 1:2:5
Most Upvoted Answer
If A = B/2 = C/5, then A : B : C isa)3 : 5 : 2b)2 : 5 : 3c)1 : 2 : 5d)...
Solution:
Let us assume the value of A, B and C as follows:
A = x
B = 2x (as A = B/2)
C = 5x (as A = C/5)
Now, we need to find the ratio of A, B and C
A:B:C = x : 2x : 5x
= 1:2:5
Hence, the correct answer is option (c) 1:2:5.
Explanation:
Given that A = B/2 and A = C/5
Let us assume that A, B and C are in the ratio of p:q:r respectively.
Then we can write:
A = (p/(p+q+r)) * k
B = (q/(p+q+r)) * k
C = (r/(p+q+r)) * k
where k is some constant.
Now, substituting the given values of A, B and C, we get:
(p/(p+q+r)) * k = (q/(p+q+r)) * 2k
(p/(p+q+r)) * k = (r/(p+q+r)) * 5k
Simplifying the above equations, we get:
p : q = 1 : 2
p : r = 1 : 5
Multiplying both the equations, we get:
p^2 : qr = 1 : 10
Since we know that p+q+r = k, we can assume any value of k and solve for p, q and r.
Let us assume k = 8, then p+q+r = 8.
Using the equation p : q = 1 : 2, we get p = 2, q = 4 and r = 2.
Therefore, the ratio of A, B and C is 2 : 4 : 10, which can be simplified to 1 : 2 : 5.
Hence, the correct answer is option (c) 1:2:5.
Let us assume the value of A, B and C as follows:
A = x
B = 2x (as A = B/2)
C = 5x (as A = C/5)
Now, we need to find the ratio of A, B and C
A:B:C = x : 2x : 5x
= 1:2:5
Hence, the correct answer is option (c) 1:2:5.
Explanation:
Given that A = B/2 and A = C/5
Let us assume that A, B and C are in the ratio of p:q:r respectively.
Then we can write:
A = (p/(p+q+r)) * k
B = (q/(p+q+r)) * k
C = (r/(p+q+r)) * k
where k is some constant.
Now, substituting the given values of A, B and C, we get:
(p/(p+q+r)) * k = (q/(p+q+r)) * 2k
(p/(p+q+r)) * k = (r/(p+q+r)) * 5k
Simplifying the above equations, we get:
p : q = 1 : 2
p : r = 1 : 5
Multiplying both the equations, we get:
p^2 : qr = 1 : 10
Since we know that p+q+r = k, we can assume any value of k and solve for p, q and r.
Let us assume k = 8, then p+q+r = 8.
Using the equation p : q = 1 : 2, we get p = 2, q = 4 and r = 2.
Therefore, the ratio of A, B and C is 2 : 4 : 10, which can be simplified to 1 : 2 : 5.
Hence, the correct answer is option (c) 1:2:5.
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