averages

[pemdas]

The ratio of two positive numbers is 3 to 4. If k is added to each number the new ratio will be 4 to 5, and the sum of the numbers will be 117. What is the value of k?

A. 1
B. 13
C. 14
D. 18
E. 21

source: Magoosh

OA later

[Anurag@Gurome]

The ratio of two positive numbers is 3 to 4. If k is added to each number the new ratio will be 4 to 5, and the sum of the numbers will be 117. What is the value of k?

A. 1
B. 13
C. 14
D. 18
E. 21

source: Magoosh

OA later

Let A : B = 3x : 4x, where x is some positive integer.
When k is added, (3x + k) : (4x + k) = 4 : 5
15x + 5k = 16x + 4k
k = x
Sum of the numbers is 117, so 3x + k + 4x + k = 117 or 7x + 2k = 117
But since k = x, so 9k = 117 implies k = 13

The correct answer is B.

[GMATGuruNY]

The ratio of two positive numbers is 3 to 4. If k is added to each number the new ratio will be 4 to 5, and the sum of the numbers will be 117. What is the value of k?

A. 1
B. 13
C. 14
D. 18
E. 21

source: Magoosh

OA later

Since a known value (117) is given for the second ratio of 4:5, draw a RATIO BOX for this ratio:

__________X____Y____Total

Ratio:_____4____5_____9

Multiplier:

Actual:_______________117


The multiplier for the box = 117/9 = 13, implying that X=52 and Y=65:

____________X_____Y______Total

Ratio:_______4_____5_______9

Multiplier:___13____13______13

Actual:_____52____65_____117


Now plug in the answer choices, which represent the value of k.
When the correct answer choice is subtracted from 52 and 65, the resulting ratio will be 3:4.

Only answer choice B works: k=13.
(52-13) : (65-13) = 39:52 = 3:4.

The correct answer is B.

[ArunangsuSahu]

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