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# What percent of b is a? (1) (b - a)b = 2/5 (2) b = 50

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What percent of b is a? (1) (b - a)b = 2/5 (2) b = 50  [#permalink]

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26 Nov 2019, 22:56
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What percent of b is a?

(1) $$\frac{b-a}{b}=\frac{2}{5}$$

(2) $$b=50$$

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Re: What percent of b is a? (1) (b - a)b = 2/5 (2) b = 50  [#permalink]

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27 Nov 2019, 00:03
1
What percent of b is a?
Let x% of b is a
—> x/100*b = a
—> x = 100a/b

(1) (b - a)/b = 2/5
—> 1 - a/b = 2/5
—> a/b = 1 - 2/5 = 3/5

So, x = 100*3/5 = 60 —> Sufficient

(2) b = 50
Nothing can be said about “a” —> Insufficient

IMO Option A

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Re: What percent of b is a? (1) (b - a)b = 2/5 (2) b = 50  [#permalink]

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27 Nov 2019, 00:41
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What percent of b is a...........i.e a/b value

(1) b−a/b=2/5.......5b-5a=2b, 3b=5a, a/b= 3/5 = 60%.............SUFFICIENT

(2) b=50..........INSUFFICIENT

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Re: What percent of b is a? (1) (b - a)b = 2/5 (2) b = 50  [#permalink]

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27 Nov 2019, 06:24
1
We are to determine the percentage of b with respect to a.
In order to do the aforementioned task, it is imperative to know either the values of a and b or the relationship between a and b.

Statement 1: (b-a)/b = 2/5
Statement 1 is sufficient. we can tell that b=5. and if b-a=2, then a=3. Hence we can determine the percentage of b with respect to a.

Statement 2: b=50
This is not sufficient since we don't have any information on the value of a. Therefore a can assume infinitely many values that can lead to different percentages.

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Re: What percent of b is a? (1) (b - a)b = 2/5 (2) b = 50  [#permalink]

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27 Nov 2019, 07:02
1
A
b*(k/100)= a
k= 100(a/b)
From first a/b can be calculated.
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Re: What percent of b is a? (1) (b - a)b = 2/5 (2) b = 50  [#permalink]

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27 Nov 2019, 07:33
1
x/100*b = a
x= a*100/b
#1
b−a/b=2/5
a/b = 3/5
sufficient
#2
b=50
insufficient
IMO A

What percent of b is a?

(1) b−a/b=2/5

(2) b=50
Math Expert
Joined: 02 Aug 2009
Posts: 8300
Re: What percent of b is a? (1) (b - a)b = 2/5 (2) b = 50  [#permalink]

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27 Nov 2019, 07:36
1
What percent of b is a?

This can be written as $$a=\frac{x}{100}*b....x=100*\frac{a}{b}$$
So we require to know the value of $$\frac{a}{b}$$.

(1) $$\frac{b-a}{b}=\frac{2}{5}.........1-\frac{a}{b}=\frac{2}{5}.........1-\frac{2}{5}=\frac{3}{5}=\frac{a}{b}.........$$

(2) $$b=50$$..Nothing about a.

A
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Re: What percent of b is a? (1) (b - a)b = 2/5 (2) b = 50  [#permalink]

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27 Nov 2019, 07:39
1
We need to know a/b or b/a to determine what percentage of b is a.

(1) (b-a)/b = 2/5
This statement gives us information about a/b and thus, we can determine what percentage of b is a.
SUFFICIENT

(2) b=50
We don't know a and hence, we can't determine what percentage of b is a.
NOT SUFFICIENT.

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Re: What percent of b is a? (1) (b - a)b = 2/5 (2) b = 50  [#permalink]

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27 Nov 2019, 09:52
1
Statement 1 is sufficient. We can transform the equation and get a/b:
$$\frac{(b-a)}{b} = \frac{2}{5}$$
$$1 - \frac{a}{b} = \frac{2}{5}$$
$$\frac{a}{b} = 1 - \frac{2}{5} = \frac{3}{5} =\frac{6}{10}$$

From the above we know that a = 60% of b.

Statement 2 is not sufficient, because a is not given.

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Re: What percent of b is a? (1) (b - a)b = 2/5 (2) b = 50  [#permalink]

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27 Nov 2019, 15:03
1
What percent of b is a?
—>$$( \frac{x}{100})*b= a$$
$$x = 100(\frac{a}{b})$$ ???

(Statement1): $$\frac{(b—a)}{b}= \frac{2}{5}$$
$$1–(\frac{a}{b}) = \frac{2}{5}$$
$$(\frac{a}{b}) = \frac{3}{5}$$
—> $$x= 100(\frac{a}{b})= 100(\frac{3}{5})= 60$$
Sufficient

(Statement2): b= 50
$$x= 100(\frac{a}{b})= 100(\frac{a}{50})= 2a$$
No info about what a is.
—> a could be any number
Insufficient

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Re: What percent of b is a? (1) (b - a)b = 2/5 (2) b = 50   [#permalink] 27 Nov 2019, 15:03
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