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John invested part of his savings into a investment X that earned
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06 May 2015, 08:38
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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
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Re: John invested part of his savings into a investment X that earned
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07 May 2015, 04:29
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 OutWe 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
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06 May 2015, 10:10
X(1+10/100) + Y(115/100) = X+Y this gives 2X = 3Y or X/Y = 3/2 So, fraction invested in X = 3/5



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Re: John invested part of his savings into a investment X that earned
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07 May 2015, 23:12
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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John invested part of his savings into a investment X that earned
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06 Jul 2015, 10:50
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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Re: John invested part of his savings into a investment X that earned
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31 Jul 2015, 04:44
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



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Re: John invested part of his savings into a investment X that earned
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31 Jul 2015, 07:05
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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John invested part of his savings into a investment X that earned
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24 Feb 2017, 07:31
what about this equation
\(\frac{110}{100}x = \frac{85}{100}(1x)\) can we solve it like this somehow?
Any thoughts on this?



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Re: John invested part of his savings into a investment X that earned
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26 Feb 2017, 21:58
iliavko wrote: what about this equation
\(\frac{110}{100}x = \frac{85}{100}(1x)\) 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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Re: John invested part of his savings into a investment X that earned
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07 Oct 2017, 06:32
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 = \(\frac{3}{5}\) Answer Choice A
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Re: John invested part of his savings into a investment X that earned
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22 Oct 2018, 09:48
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Re: John invested part of his savings into a investment X that earned
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