Two numbers are in the ratio of 2:3 . if 4 is added in both numbers

Question

Two numbers are in the ratio of 2:3 . if 4 is added in both numbers the ratio becomes 5:7. Find the difference between numbers.

A. 8
B. 6
C. 4
D. 2
E. 10

Abhishek009 · Accepted Answer

\frac{2x + 4}{3x + 4} = \frac{5}{7}

Or,  14x + 28 = 15x + 20

Or,  x = 8

Now, we know  3x - 2x = x = 8

So, The answer must be (A) 8

BrentGMATPrepNow · Answer

One option is to use 2 variables, x and y

Two numbers are in the ratio of 2:3  
So, x/y = 2/3
Cross multiply to get: 3x = 2y
Rewrite as  3x - 2y = 0

If 4 is added in both numbers the ratio becomes 5:7  
So, (x + 4)/(y + 4) = 5/7
Cross multiply to get: 7(x + 4) = 5(y + 4)
Expand to get: 7x + 28 = 5y + 20
Rewrite as  7x - 5y = - 8

We now have two equations: 
 7x - 5y = - 8 
 3x - 2y = 0

IMPORTANT: the question asks us to find the DIFFERENCE (either x - y or y - x), so we don't necessarily have to solve for x and for y.

Take  bottom equation  and multiply both sides to get an EQUIVALENT equation:
 7x - 5y = - 8 
 6x - 4y = 0

Now subtract the bottom equation from the top equation to get: x - y = -8
This also means that y - x = 8
So, the DIFFERENCE = 8

Answer: A

Cheers,
Brent

EMPOWERgmatRichC · Answer

Hi ske,

While this question can be solved algebraically, it can also be solved with a bit of brute force and some Number Properties.

We're told that two numbers are in the ratio of 2:3. Thus, the two numbers could be...
2 and 3
4 and 6
6 and 9
8 and 12
10 and 15
Etc.

We're told that ADDING 4 to each number changes the ratio of the numbers to 5:7. We're asked for the DIFFERENCE between the original numbers.

Since adding 4 makes the first number a multiple of 5, this limits the possibilities....
2+4 = 6 NOT POSSIBLE
4+4 = 8 NOT POSSIBLE
6+4 = 10 This IS possible...Using this example, we would have...

"6 and 9", after adding 4 to each, becomes "10 and 13"...this is NOT a ratio of 5 to 7 though (even though it's pretty close), so we have to keep looking....

The next value that becomes a multiple of 5 when you add 4 to it is...16...
16 + 4 = 20

With "16 and 24", after adding 4 to each, we have "20 and 28." This IS a ratio of 5 to 7, so we have our pair of original numbers.

The difference between them is 8.

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

MathRevolution · Answer

Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

Two numbers are in the ratio of 2:3 . if 4 is added in both numbers the ratio becomes 5:7. Find the difference between numbers.

A 8

B 6

C 4

D 2

E 10

Let two numbers be a and b.

Since a:b=2:3, we have 2b=3a --> a=2k and b=3k.

So the difference of a and b is k(=3k-2k).

By the assumption in the question we have (2k+4):(3k+4) = 5:7.

That means 5*(3k+4)=7*(2k+4) ---> 15k+20=14k+28 ---> k=8.

The answer is, therefore, A.

ramajha · Answer

As after adding 4 numbers ratio becomes 5:7 so i checked for   * 2 or 3 or 4 so for 4, 20-4/28-4=16/24=2/3 so required numbers are 20 & 28 so difference is 8 option A

EMPOWERgmatRichC · Answer

Hi ramajha,

Your approach is also valid. When dealing with ratio questions on the GMAT, there are usually more ways than you might realize to get to the correct answer (some Tactical, some Algebraic, and some that are just 'brute force' arithmetic). Since no-one will ever know how you got the correct answer, you should use whatever approach you find to be fastest/easiest.

GMAT assassins aren't born, they're made,
Rich

mindi · Answer

adding 4 numbers ratio becomes 5:7 so i checked for   * 2 or 3 or 4 so for 4, 20-4/28-4=16/24=2/3 so required numbers are 20 & 28 so difference is 8 option A

generis · Answer

I solved similarly to  Abhishek009  , with one different step.

\frac{2x + 4}{3x +
4}  =  \frac{5}{7} . Cross multiply to get

14x + 28 = 15x + 20

x = 8, which is the multiplier for the original ratio

So original ratio is

\frac{(2)(8)}{(3)(8)}  =  \frac{16}{24}  (Don't reduce - need original #s)

24 - 16 = 8

Answer A

noushy · Answer

Let the no.s be 2x & 3x

so, 2x+4/3x+4= 5/7
14x+28=15x+20
x=8

difference= 3(8)-2(8)= 8 (Ans)

Two numbers are in the ratio of 2:3 . if 4 is added in both numbers

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Two numbers are in the ratio of 2:3 . if 4 is added in both numbers

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