Question

Mr. Peter gave his eldest son David a bag with 1000 gold coins. David took 230 gold coins from the bag and gave the rest to his younger brothers John, Joe and Jonathan, and advised them to distribute the balance left in the bag amongst themselves in proportion to their age which together amounted to 17.5 years. After a lot of deliberation and discussion John, Joe and Jonathan came to a conclusion to distribute the gold coins. Their methodology was as follows: As often John took 4 gold coins, Joe took 3. As often John took 6 gold coins Jonathan took 7. What was the age of John, Joe and Jonathan ?

• A. 6 years, 4.5 years and 7 years respectively
• B. 5 years, 5.5 years and 7 years respectively
• C. 6 years, 5 years and 6.5 years respectively
• D. 5 years, 6.5 years and 6 years respectively

Answer 1

The Correct Option is A

To solve the problem, we need to find the ages of John, Joe, and Jonathan based on the distribution of gold coins. David started with 1000 gold coins and took 230 coins, leaving 770 coins to be distributed among his younger brothers according to their ages. Their ages must sum to 17.5 years. Let's use variables:

• Let the ages of John, Joe, and Jonathan be J, E, and N respectively.
• Given: J + E + N = 17.5 

Now, follow the distribution constraints:

• When John takes 4 coins, Joe takes 3 coins. Therefore, the proportion of coins taken by John to those taken by Joe is 4:3.
• When John takes 6 coins, Jonathan takes 7 coins. Therefore, the proportion of coins taken by John to those taken by Jonathan is 6:7.

Convert these proportions into equations:

• Let k be a common multiple for all distributions. Since John always takes a relative amount, set his portion as a baseline: John takes 4k coins, Joe takes 3k coins. Also, John takes 6m coins, and Jonathan takes 7m coins.
• Since coins come from the same pool distributed in said proportions:
• 4k/6m = J/N = 2/3.5 => k/m = 1/1.
• This implies k = m (same). So, total distribution can be represented as 4x + 3x + 6x + 7x = 20x.

The total number of coins from both pairings:

• 770 = 20x, therefore x = 38.5.
• Now John takes 4x = 154 coins, Joe takes 3x = 115.5 coins, Jonathan takes 7x = 269.5 coins.
• Divide coins by x to find relative distribution based on age proportion: John gets 154/38.5 = 4 years, Joe gets 115.5/38.5 = 3 years, Jonathan gets 269.5/38.5 = 7 years.

The ages proportion according to the ratio:

• Therefore John = 6 years, Joe = 4.5 years, Jonathan = 7 years.
• The total age sum is 6 + 4.5 + 7 = 17.5.

Hence the correct answer is: 6 years, 4.5 years, and 7 years respectively.