The Present Ages of Three Persons are in the Proportion of 5:8:7 GMAT Problem Solving

Question: The present ages of three persons are in the proportion of 5:8:7. Eight years ago, the sum of their ages was 76. Find the present age of the youngest person.

(A) 15
(B) 20
(C) 25
(D) 30
(E) 32

Correct Answer: C
Solution and Explanation:

Approach Solution 1:

Three people are currently 5: 8: 7 years old on average.
Therefore, the three ages COULD be 5, 8, and 7, or the three ages COULD be 10, 16, and 14, or the three ages COULD be 15, 24, and 21, or the three ages COULD be 20, 32, and 28, etc.
The three current ages are multiples of 5, 8, and 7, respectively, so take note of this.

Therefore, we could write.
Let x = the youngest person's age as of now.
Let 8x equal the oldest person's current age.
Let 7x equal the middle person's current age.

When their ages combined eight years ago, it was 76.
The ages were as follows eight years ago:
Age of youngest individual = 5x - 8
Age of oldest person divided by 8x
Age of middle person = 7x - 8

Thus, the formula is: (5x - 8) + (8x - 8) + (7x - 8) = 76.
Reduced form: 20x - 24 = 76
So, 20x = 100
Answer: x Equals 5.

5 times the youngest person's current age
Thus, the youngest person's age today is 5 + 5 + 25.

Approach Solution 2:

Three people are currently 5: 8: 7 years old on average.
Therefore, the three ages COULD be 5, 8, and 7, or the three ages COULD be 10, 16, and 14, or the three ages COULD be 15, 24, and 21, or the three ages COULD be 20, 32, and 28, etc.
The three current ages are multiples of 5, 8, and 7, respectively, so take note of this.

( 5x - 8 ) + ( 8x - 8 ) + ( 7x - 8 ) = 76
Or, 20x - 24 = 76
Or, 20x = 100
Or, x = 5

The youngest member's age as of right now is 5 x 5 = 25 years.

Approach Solution 3:

Since their aggregate was 76 eight years ago, it must now be 76 Plus eight times three, or 100.
Their current ages are 5:8:7, and we know that 5X + 8X + 7X = 100.
20X = 100 and X = 5

The oldest individual will be 5X, or 5*5 = 25. ( C)

Or

( 5x - 8 ) + ( 8x - 8 ) + ( 7x - 8 ) = 76
Or, 20x - 24 = 76
Or, 20x = 100
Or, x = 5

The youngest member's age as of right now is 5 x 5 = 25 years.

“The present ages of three persons are in the proportion of 5:8:7" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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