Answer :
Certainly! Let's break down the problem step by step:
1. Define the Variables:
- Let [tex]\( M \)[/tex] represent the current age of the man.
- Let [tex]\( S \)[/tex] represent the sum of the current ages of his two sons.
2. Formulate the Equations:
- According to the problem, the man's age is three times the sum of the ages of his two sons. Therefore, we can write:
[tex]\[ M = 3S \][/tex]
- The problem also states that five years from now, the man's age will be double the sum of the ages of his two sons. In five years, the man's age will be [tex]\( M + 5 \)[/tex] and the sum of the sons' ages will be [tex]\( S + 10 \)[/tex] (since each son will be 5 years older, contributing a total of 10 years).
Therefore, we can write:
[tex]\[ M + 5 = 2(S + 10) \][/tex]
3. Solve the System of Equations:
- Starting with the first equation:
[tex]\[ M = 3S \][/tex]
- Substitute [tex]\( M \)[/tex] from the first equation into the second equation:
[tex]\[ 3S + 5 = 2(S + 10) \][/tex]
- Expand and simplify the second equation:
[tex]\[ 3S + 5 = 2S + 20 \][/tex]
[tex]\[ 3S - 2S = 20 - 5 \][/tex]
[tex]\[ S = 15 \][/tex]
- Now substitute [tex]\( S \)[/tex] back into the first equation to find [tex]\( M \)[/tex]:
[tex]\[ M = 3S \][/tex]
[tex]\[ M = 3 \times 15 \][/tex]
[tex]\[ M = 45 \][/tex]
4. Conclusion:
The present age of the man is [tex]\( 45 \)[/tex] years.
Therefore, the correct answer is:
(D) 45 years
1. Define the Variables:
- Let [tex]\( M \)[/tex] represent the current age of the man.
- Let [tex]\( S \)[/tex] represent the sum of the current ages of his two sons.
2. Formulate the Equations:
- According to the problem, the man's age is three times the sum of the ages of his two sons. Therefore, we can write:
[tex]\[ M = 3S \][/tex]
- The problem also states that five years from now, the man's age will be double the sum of the ages of his two sons. In five years, the man's age will be [tex]\( M + 5 \)[/tex] and the sum of the sons' ages will be [tex]\( S + 10 \)[/tex] (since each son will be 5 years older, contributing a total of 10 years).
Therefore, we can write:
[tex]\[ M + 5 = 2(S + 10) \][/tex]
3. Solve the System of Equations:
- Starting with the first equation:
[tex]\[ M = 3S \][/tex]
- Substitute [tex]\( M \)[/tex] from the first equation into the second equation:
[tex]\[ 3S + 5 = 2(S + 10) \][/tex]
- Expand and simplify the second equation:
[tex]\[ 3S + 5 = 2S + 20 \][/tex]
[tex]\[ 3S - 2S = 20 - 5 \][/tex]
[tex]\[ S = 15 \][/tex]
- Now substitute [tex]\( S \)[/tex] back into the first equation to find [tex]\( M \)[/tex]:
[tex]\[ M = 3S \][/tex]
[tex]\[ M = 3 \times 15 \][/tex]
[tex]\[ M = 45 \][/tex]
4. Conclusion:
The present age of the man is [tex]\( 45 \)[/tex] years.
Therefore, the correct answer is:
(D) 45 years
