The ratio of the earnings of A,B and C is 2:3:5

Question

The ratio of the earnings of A,B and C is 2:3:5. If A increases his earnings by a certain amount, B by double that amount and C by triple that amount, then which of the following could be the lowest ratio of the earnings of A and C after the increase.
A. 7:17
B. 9:22
C. 13:40
D. 16:45
E. 19:53

14101992 · Accepted Answer

Senthil1981 
Hint: Try working back from the answer choices.

If you still are not sure how to go ahead then look at the solution below:

Let increased earning by A as x. Then increased earning by B will be 2x and C will be 3x. 
We have A:B:C as 2:3:5.
In ratio questions, take LCM of all the given value. In this case, LCM of 2,3 and 5 will be 30.
So, we can write the same ratio of A:B:C as (2*3):(3*3):(5*3) 
 
therefore, A:B:C = 6:9:15
Now we have to add x, 2x and 3x respectively to A,B and C
As question is asking for A:C ratio, we have A:C = 6+x : 15+3x

Now work back from the answer choice.

Choice A. 7:17 Put x=1. A:C=7:18. Not true
Choice B. 9:22 Put x=3. A:C=9:24. Not true
Choice C. 13:40 Put x=7. A:C=13:36 Not true
Choice D. 16:45 Put x=10. A:C=16:45 True
And we have the answer as D.

Senthil1981 · Answer

Hi,

Would you please share the source of this question. Doesn't seem like a GMAT one, since there are 2 unknown and only one equation.

mahawarchirag · Answer

Let initial earnings be 2x , 3x and 5x . After the increase incomes would be 2x+y , 3x+2y, 5x+3y .
Now we have to find possible values of 2x+y/5x+3y . Try testing by putting options as we have to find the possible solution by eliminating other options. Remember x,y >0 . so the relation between them we get after equating the above ratio with one of the options should give a positive correlation between x & y which is given only by option D . where 10x=3y

HiLine · Answer

Let's say A starts out with 2, and C with 5.

Let's also assume that the amount by which A increases is 16.

So A becomes: 2+16 = 18
C becomes: 5 + 3x16 = 53

Now let's say A starts out with 6, and C with 15

Let's also assume that the amount by which A increases is 10.

So A becomes: 6+10 = 16
C becomes: 15 + 3x10 = 45

So both answer choices D and E are acceptable, which implies that the question itself is not.

14101992 · Answer

HiLine 
Correctly pointed out. Sorry for the typo. Have corrected the same in the question.

KarishmaB · Answer

Please check the question. If it is an MGMAT question (as tagged), please put up a screenshot. Two options (both (D) and (E)) are possible as answers.

The ratio of A:C = 2:5. An amount x is added to A and 3x is added to C. So the new ratio is:

2a + x : 5a + 3x

Note that 3 * (2a + x) = 6a + 3x which is more than 5a + 3x.
So if in any option, 3 times the first number is equal to or less than the second number, we should eliminate it. (C) eliminated.

Now note that 2.5 * (2a + x) = 5a + 2.5x
So if in any option, 2.5 times the first number is equal to or less than the second number, we should eliminate it. 
(A) 2.5*7 = 14 + 3.5 = 17.5 (eliminated)
(B) 2.5*9 = 18 + 4.5 = 22.5 (eliminated)

(D) 2.5*16 = 32 + 8 = 40 (keep). Here, 0.5x = 5 so x = 10, a = 3 (satisfies)
(E) 2.5*19 = 38 + 9.5 = 47.5 (keep). Here, 0.5x = 5.5 so x = 11, a = 4 (satisfies)

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The ratio of the earnings of A,B and C is 2:3:5

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