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Manager  P
Joined: 13 Jun 2012
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Location: United States
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John invested part of his savings into a investment X that earned  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 72% (02:05) correct 28% (02:39) wrong based on 266 sessions

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John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment Y that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?

a. 3/5
b.2/3
c.7/10
d.3/4
e.4/5
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3078
Re: John invested part of his savings into a investment X that earned  [#permalink]

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Given:
We are given information about John investing his savings in investment X and Y such that he made 10% profit in investment X and 15% loss in investment Y. We are also told that John did not make any profit or loss on his total investment in X & Y. We are asked to find the ratio of his investment in X to his total investment.

Approach:
We are told that John invested in investment X & Y only.Let's assume his investment in X to be $$x$$ and investment in Y to be $$y$$.

So, we need to find $$\frac{x}{x+y}$$

For finding the above ratio we need to find a relation between $$x$$ and $$y$$. Let's use the information given in the question to find out the same.

Profit made by John in investment X = 10% of amount invested in X = 10% of $$x$$

Loss made by John in investment Y = 15% of amount invested in Y = 15% of y

Since he did not make any profit or loss on his investments in X & Y that would mean his profit on investment X is equal to his loss in investment Y i.e. 10% of $$x$$ = 15% of $$y$$.

We now have a relation between $$x$$ and $$y$$. We will use this relation to find the ratio of his investment in X to his total investment.

Working Out
We know that 10% of $$x$$ = 15% of $$y$$

$$0.1x = 0.15y$$ i.e. $$x = \frac{3y}{2}$$. From here, we can write $$y = \frac{2x}{3}$$

Hence $$\frac{x}{x+y}$$ = $$\frac{x}{x+2x/3}$$ = $$\frac{3x}{5x}$$

= $$\frac{3}{5}$$ which is our answer

Hope its clear!

Regards
Harsh
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Re: John invested part of his savings into a investment X that earned  [#permalink]

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X(1+10/100) + Y(1-15/100) = X+Y
this gives 2X = 3Y
or X/Y = 3/2
So, fraction invested in X = 3/5
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: John invested part of his savings into a investment X that earned  [#permalink]

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Turkish wrote:
John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment Y that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?

a. 3/5
b.2/3
c.7/10
d.3/4
e.4/5

Just use weighted averages. Profit of 10% on X and profit of -15% on Y combine to give profit on 0% on total.
Wx/Wy = (Py - Pavg)/(Pavg - Px) = (-15 - 0)/(0 - 10) = 3/2

So X is 3/5 of the total amount invested.

For more on this weighted averages formula, check: http://www.veritasprep.com/blog/2011/03 ... -averages/
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SVP  V
Status: It's near - I can see.
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Location: India
Concentration: International Business, Operations
Schools: INSEAD Jan '19
GPA: 3.01
WE: Engineering (Real Estate)
John invested part of his savings into a investment X that earned  [#permalink]

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VeritasPrepKarishma wrote:
Turkish wrote:
John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment Y that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?

a. 3/5
b.2/3
c.7/10
d.3/4
e.4/5

Just use weighted averages. Profit of 10% on X and profit of -15% on Y combine to give profit on 0% on total.
Wx/Wy = (Py - Pavg)/(Pavg - Px) = (-15 - 0)/(0 - 10) = 3/2

So X is 3/5 of the total amount invested.

For more on this weighted averages formula, check: http://www.veritasprep.com/blog/2011/03 ... -averages/

These links of Quarter Wit, Quarter Wisdom are really helpful. Very easy to understand and very clear. Thanx...Can we use weighted avg. concept in DS questions effectively?
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Director  G
Joined: 23 Jan 2013
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Re: John invested part of his savings into a investment X that earned  [#permalink]

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1
Algebra is:

1.1x+0.85y=x+y, where x and y are two parts of investments

0.1x=0.15y => x/y=0.15/0.1 or 15/10. So x/x+y=15/25=3/5

A
Senior Manager  B
Joined: 28 Jun 2015
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Concentration: Finance
GPA: 3.5
Re: John invested part of his savings into a investment X that earned  [#permalink]

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X(10) --- Net(0) --- Y(-15) = -15/-10 = 3/2.

So, John invested 3/3+2 = 3/5 of his savings in investment X. Ans (A).
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Senior Manager  S
Joined: 08 Dec 2015
Posts: 285
GMAT 1: 600 Q44 V27 John invested part of his savings into a investment X that earned  [#permalink]

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$$\frac{110}{100}x = \frac{85}{100}(1-x)$$ can we solve it like this somehow?

Any thoughts on this?
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: John invested part of his savings into a investment X that earned  [#permalink]

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iliavko wrote:

$$\frac{110}{100}x = \frac{85}{100}(1-x)$$ can we solve it like this somehow?

Any thoughts on this?

This is not correct. Say he invested a fraction x in investment X. Since he made no profit no loss, it means that whatever he earned as profit, that is exactly what he lost.

So, profit = loss
$$\frac{10}{100} * x = \frac{15}{100} * (1 - x)$$
x = 3/5

When you write the equation as written by you above, you are saying that the amount obtained from investment X is the same as that obtained from investment Y. That is actually not the case. Say if 60 were invested in investment X and 40 in investment Y, the amount obtained from investment X would be 66 and the amount obtained from investment Y would be 34. The point is that the profit and loss are equal. So profit = 6, loss = 6. That is what you have to equate.

Hope this is clear.
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Manager  G
Joined: 12 Jun 2016
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Location: India
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Re: John invested part of his savings into a investment X that earned  [#permalink]

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Here's how I approached this question. I hope this is correct.

Since John made neither profit nor loss, he gained as much as he lost. Let the amount invested by John in X and Y be $$x$$ and $$y$$.

We have

$$10x = 15y$$

$$2x = 3y$$

$$\frac{x}{y} = \frac{3}{2}$$

Therefore share of x = $$\frac{3}{5}$$

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Re: John invested part of his savings into a investment X that earned  [#permalink]

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_________________ Re: John invested part of his savings into a investment X that earned   [#permalink] 22 Oct 2018, 09:48
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