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The ratio of incomes of a and b is 3:4 and ratio of their expenditure is 4:5 . what can be their possible ratio of savings 9:10 or 3:4 or 4:5 or 13:20. I don't find anything suitable in the options I think the answer is 2:3 but it has to be from the choices.

Gregory Grant
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tapadia newlon
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  • You are looking for the ratio: $\dfrac{a-c}{b-d}$. With $a = 0.75b, c = 0.8d$, can you take it from here? – DeepSea May 25 '15 at 13:13

1 Answers1

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We can scale everything in terms of A's income, so call that $1$. B's income is then $\frac 43$. Let A's expenses be $x$, which makes B's expenses $\frac 54x$. A's savings are $1-x$, while B's are $\frac 43-\frac 54x$, giving a ratio of $\frac {1-x}{\frac 43-\frac 54x}=\frac {12-12x}{16-15x}$. We are now asked which of the given ratios can match this fraction. If $x=0$, so there are no expenses, the ratio is $3:4$. I think you are supposed to think this is not possible. As $x$ increases toward $1$, the ratio decreases toward zero. The only choice that is less than $3:4$ is $13:20$ so that must be the intended answer.

However, if I solve $\frac {12-12x}{16-15x}=\frac 9{10}$ I get a perfectly good answer of $x=\frac 85$. In that cases both peoples expenses exceed their income. A is saving $-\frac 35$ and B is saving $-\frac 23$, which gives the proper ratio. We cannot get a ratio of $\frac 45$, but can get as close as we want if $x$ gets very large.

Ross Millikan
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