Latest CAT Aptitude Question SOLUTION: B as a percentage of A is equal to A as a percentage of (A + B). Find B as a percentage of A

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(#M40025651) CAT Numerical Ability question Percent Keep an EYE

B as a percentage of A is equal to A as a percentage of (A + B). Find B as a percentage of A

Asked In CAT MAN (10 years ago)

Unsolved Read Solution (2)

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Read Solution (2) :

dishant goel  (5 years ago)

From the question stem, we know
B
A
=(
A
A+B
) --------------- (1)

As B is a percent of A, let us assume B=Ax
Then, equation (1) can be re-written as x=(
1
1+x
)
⇒ x(1+x)=1

solving, we get x2+x−1=0

⇒ x=(
−1+√5
2
) or x=(
−1−√5
2
)
So, x=(
−1+√5
2
)=
1.24
2


Or 0.62 = 62%

Is this solution Helpfull? Yes | No   

nilakshi dashpute  (5 years ago)

From the question stem, we know
B
A
=
(
A
A
+
B
)
--------------- (1)

As B is a percent of A, let us assume
B
=
A
x

Then, equation (1) can be re-written as
x
=
(
1
1
+
x
)

⇒
x
(
1
+
x
)
=
1


After this step, trial and error works best. The solution is 62%, answer choice (A) is the correct one.

Alternatively, solving, we get
x
2
+
x
−
1
=
0

⇒
x
=
(
−
1
+
5
2
)
or
x
=
(
−
1
−
5
2
)

So,
x
=
(
−
1
+
5
2
)
=
1.24
2


Or 0.62 = 62%

Is this solution Helpfull? Yes | No   

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