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The age of a person is twice the sum of ages of his two sons and five years ago his age was thrice the sum of their ages .fing his present age?
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The age of a person is twice the sum of ages of his two sons and five ...
Problem Analysis:
The problem provides information about the relationship between a person's age and the ages of his two sons. By setting up equations based on the given conditions, we can solve for the person's present age.
Given Information:
Let the person's age be P and the ages of his two sons be S1 and S2.
According to the problem:
1. P = 2(S1 + S2)
2. P - 5 = 3(S1 + S2)
Solution:
1. Substitute the first equation into the second equation:
2(S1 + S2) - 5 = 3(S1 + S2)
2S1 + 2S2 - 5 = 3S1 + 3S2
2S1 + 2S2 - 3S1 - 3S2 = 5
-S1 - S2 = 5
2. Substitute S1 = P/2 - S2 into the above equation:
-(P/2 - S2) - S2 = 5
-P/2 + S2 - S2 = 5
-P/2 - 2S2 = 5
-P - 4S2 = 10
P = 10 + 4S2
3. Since P = 2(S1 + S2), substitute P = 10 + 4S2 into this equation:
10 + 4S2 = 2(S1 + S2)
10 + 4S2 = 2(S1) + 2(10 - S1)
10 + 4S2 = 2S1 + 20 - 2S1
4S2 = 10
S2 = 10/4 = 2.5
4. Substitute S2 = 2.5 into P = 10 + 4S2:
P = 10 + 4(2.5)
P = 10 + 10
P = 20
Therefore, the person's present age is 20 years old.
The problem provides information about the relationship between a person's age and the ages of his two sons. By setting up equations based on the given conditions, we can solve for the person's present age.
Given Information:
Let the person's age be P and the ages of his two sons be S1 and S2.
According to the problem:
1. P = 2(S1 + S2)
2. P - 5 = 3(S1 + S2)
Solution:
1. Substitute the first equation into the second equation:
2(S1 + S2) - 5 = 3(S1 + S2)
2S1 + 2S2 - 5 = 3S1 + 3S2
2S1 + 2S2 - 3S1 - 3S2 = 5
-S1 - S2 = 5
2. Substitute S1 = P/2 - S2 into the above equation:
-(P/2 - S2) - S2 = 5
-P/2 + S2 - S2 = 5
-P/2 - 2S2 = 5
-P - 4S2 = 10
P = 10 + 4S2
3. Since P = 2(S1 + S2), substitute P = 10 + 4S2 into this equation:
10 + 4S2 = 2(S1 + S2)
10 + 4S2 = 2(S1) + 2(10 - S1)
10 + 4S2 = 2S1 + 20 - 2S1
4S2 = 10
S2 = 10/4 = 2.5
4. Substitute S2 = 2.5 into P = 10 + 4S2:
P = 10 + 4(2.5)
P = 10 + 10
P = 20
Therefore, the person's present age is 20 years old.
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The age of a person is twice the sum of ages of his two sons and five years ago his age was thrice the sum of their ages .fing his present age?
Question Description
The age of a person is twice the sum of ages of his two sons and five years ago his age was thrice the sum of their ages .fing his present age? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The age of a person is twice the sum of ages of his two sons and five years ago his age was thrice the sum of their ages .fing his present age? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The age of a person is twice the sum of ages of his two sons and five years ago his age was thrice the sum of their ages .fing his present age?.
The age of a person is twice the sum of ages of his two sons and five years ago his age was thrice the sum of their ages .fing his present age? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The age of a person is twice the sum of ages of his two sons and five years ago his age was thrice the sum of their ages .fing his present age? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The age of a person is twice the sum of ages of his two sons and five years ago his age was thrice the sum of their ages .fing his present age?.
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