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The sum of present ages of A and B is 63 years. The ratio of their ages 3 years later will be 11 : 12. What is the present age (in years) of A?
- a)30
- b)33
- c)36
- d)27
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The sum of present ages of A and B is 63 years. The ratio of their age...
Let x years be the present age of A & y years be the present age of B.
Sum of present ages = 63 → x + y = 63 …. Equation (1)
Then, After 3 years
Age of A = x + 3
Age of B = y + 3
Ratio= x + 3/y + 3 = 11/12
By solving it we get:
12x -11y = -3 …… Equation (2)
By solving equation (1) and equation (2) we get:
x = 30 & y = 33.
Hence, the present age of A is 30 years.
Sum of present ages = 63 → x + y = 63 …. Equation (1)
Then, After 3 years
Age of A = x + 3
Age of B = y + 3
Ratio= x + 3/y + 3 = 11/12
By solving it we get:
12x -11y = -3 …… Equation (2)
By solving equation (1) and equation (2) we get:
x = 30 & y = 33.
Hence, the present age of A is 30 years.
Most Upvoted Answer
The sum of present ages of A and B is 63 years. The ratio of their age...
Given information:
- The sum of present ages of A and B is 63 years.
- The ratio of their ages 3 years later will be 11:12.
Let's assume the present age of A is x years and the present age of B is y years.
Sum of present ages:
x + y = 63 ...............(1)
Ratio of ages 3 years later:
(x + 3)/(y + 3) = 11/12 ...............(2)
Solving Equations (1) and (2) simultaneously:
Multiplying both sides of Equation (2) by 12(y + 3):
12(x + 3) = 11(y + 3)
12x + 36 = 11y + 33
12x - 11y = -3 ...............(3)
Now, we can solve Equations (1) and (3) simultaneously to find the values of x and y.
First, let's multiply Equation (1) by 11:
11(x + y) = 11(63)
11x + 11y = 693 ...............(4)
Subtracting Equation (3) from Equation (4):
11x + 11y - (12x - 11y) = 693 - (-3)
11x + 11y - 12x + 11y = 693 + 3
-1x + 22y = 696
x - 22y = -696 ...............(5)
Adding Equations (3) and (5):
(x - 22y) + (12x - 11y) = -696 - 3
13x - 33y = -699
13x = 33y - 699
x = (33y - 699)/13
Now, we need to find a value of y that satisfies both Equations (1) and (5).
Let's substitute the value of x in Equation (1):
(33y - 699)/13 + y = 63
33y - 699 + 13y = 63 * 13
46y - 699 = 819
46y = 819 + 699
46y = 1518
y = 1518/46
y ≈ 33
So, the present age of B is approximately 33 years.
Now, substituting the value of y in Equation (1):
x + 33 = 63
x = 63 - 33
x = 30
Therefore, the present age of A is 30 years.
- The sum of present ages of A and B is 63 years.
- The ratio of their ages 3 years later will be 11:12.
Let's assume the present age of A is x years and the present age of B is y years.
Sum of present ages:
x + y = 63 ...............(1)
Ratio of ages 3 years later:
(x + 3)/(y + 3) = 11/12 ...............(2)
Solving Equations (1) and (2) simultaneously:
Multiplying both sides of Equation (2) by 12(y + 3):
12(x + 3) = 11(y + 3)
12x + 36 = 11y + 33
12x - 11y = -3 ...............(3)
Now, we can solve Equations (1) and (3) simultaneously to find the values of x and y.
First, let's multiply Equation (1) by 11:
11(x + y) = 11(63)
11x + 11y = 693 ...............(4)
Subtracting Equation (3) from Equation (4):
11x + 11y - (12x - 11y) = 693 - (-3)
11x + 11y - 12x + 11y = 693 + 3
-1x + 22y = 696
x - 22y = -696 ...............(5)
Adding Equations (3) and (5):
(x - 22y) + (12x - 11y) = -696 - 3
13x - 33y = -699
13x = 33y - 699
x = (33y - 699)/13
Now, we need to find a value of y that satisfies both Equations (1) and (5).
Let's substitute the value of x in Equation (1):
(33y - 699)/13 + y = 63
33y - 699 + 13y = 63 * 13
46y - 699 = 819
46y = 819 + 699
46y = 1518
y = 1518/46
y ≈ 33
So, the present age of B is approximately 33 years.
Now, substituting the value of y in Equation (1):
x + 33 = 63
x = 63 - 33
x = 30
Therefore, the present age of A is 30 years.
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