Form a pair of linear equation in two variables, taking your present age as 'X' and your Father's/Mother's age as 'y' form the first equation and form another equation by taking your age 5 years ago and your Father's /Mother's age 5 years ago.
1. Solve the equations using elimination method. by taking my present age 15 and fathers present age 54
Answers
Answer:
Suppose that the present age of the son is = x years. Then the father’s age is (60 -x) years. Notice that we are trying to reduce the problem into as few variables as possible. As per the second condition of the question, we have:
The age of the father six years ago = (60 – x) – 6 years = 54 – x years.
Similarly the age of the son six years ago will be x – 6 years. Therefore as per the second condition, we have;
54 – x = 5(x – 6) or 54 – x = 5x – 30 and we can write 6x = 84
Hence, we have x = 14 years. Thus the son’s age after 6 years = (x+ 6) = (14 + 6) = 20 years. Hence the correct option is C) 20 years.
More Solved Examples
Example 2: The difference in the age of two people is 20 years. If 5 years ago, the elder one of the two was 5 times as old as the younger one, then their present ages are equal to:
A) 20 and 30 years respectively
B) 30 and 10 years respectively
C) 15 and 35 years respectively
D) 32 and 22 years respectively
Answer: The first step is to find the equation. Let the age of the younger person be x. Then the age of the second person will be (x + 20) years. Five years ago their ages would have been x – 5 years and x + 20 years. Therefore as per the question, we have: 5 (x – 5) = (x + 20 – 5) or 4x = 40 or x = 10.
Therefore the ages are 10 years for the younger one and (10 + 20) years = 30 years for the elder one.
Example 3: Yasir is fifteen years elder than Mujtaba. Five years ago, Yasir was three times as old as Mujtaba. Then Yasir’s present age will be:
A) 29 years B) 30 years C) 31 years D) 32 years
Answer: Let the age of Yasir be = x years. Then the age of Mujtaba will be equal to x – 15 years. Now let us move on to the second condition. Five years ago the age of Yasir will be equal to x – 5 years. Also, the age of Mujtaba five years ago will be x – 15 – 6 years = x – 21 years. As per the question, we have:
3(x – 21) = x – 5 or 3x – 63 = x – 5. Therefore we have: 2x = 58 and hence x = 29 years. Therefore Yasir’s present age is 29 years and the correct option is A) 29 years.
Example 4: Ten years ago, the age of a person’s mother was three times the age of her son. Ten years hence, the mother’s age will be two times the age of her son. The ratio of their present ages will be:
A) 10:19 B) 9: 5 C) 7: 4 D) 7: 3
Answer: Let the age of the son ten years ago be equal to x years. Therefore the age of the mother ten years ago will be equal to 3x. Following this logic, we see that the present age of the son will be equal to x + 10 years and that of the mother will be equal to 3x + 10 years.
The second condition says that ten years from the present, the mother’s age will be twice that of her son. After ten year’s the mother’s age will be 3x + 10 + 10 years and that of the son will be x + 10 + 10 years. As per the question we have:
(3x + 10) +10 = 2 [(x + 10) + 10] or (3x + 20) = 2[x + 20]. In other words, we can write:
x = 20 years. Thus the present age of the mother = 3(20) + 10 = 70 years. Also the present age of the son = 20 + 10 = 30 years. Thus the ratio is 7:3 and the correct option is D)
Therefore after solving the equations we get X = 15 and Y = 54.
Given:
My present age = X years
My Father's present age = Y years
First Equation: My age 5 years ago.
Second Equation: My father's age 5 years ago.
To Find:
Solution of the formed equations using elimination method when my present age is 15 years and my father's age is 54
Solution:
The given question can be solved very easily as shown below.
Given that:
My present age = X years
My Father's present age = Y years
First equation: X - 5 = 15 - 5 ⇒ X = 15
Second Equation: Y - 5 = 54 - 5 = 54
By Elimination method,
⇒ X + 0 = 15
⇒ 0 + Y = 54
Here elimination method is not needed because each equation is solved already.
Therefore after solving the equations we get X = 15 and Y = 54.
#SPJ2