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The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. What is the present age of the husband?
- a)40
- b)32
- c)28
- d)30
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The average age of husband, wife and their child 3 years ago was 27 ye...
Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of wife and child (20 x 2 + 5 x 2) years = 50 years.
Husband's present age = (90 - 50) years = 40 years.
Most Upvoted Answer
The average age of husband, wife and their child 3 years ago was 27 ye...
(h-3 + w-3 + c-3 )/3=27 or, h+w+c=90 & (w+c -10)/2=20, or, w+c=50 so, now, h=40
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Community Answer
The average age of husband, wife and their child 3 years ago was 27 ye...
To solve this problem, let's assume the present age of the husband, wife, and child as H, W, and C respectively.
**Step 1: Understand the given information**
According to the question, 3 years ago, the average age of the husband, wife, and child was 27 years. This means that if we subtract 3 from the present age of each person and take the average, it should be equal to 27.
Similarly, 5 years ago, the average age of the wife and the child was 20 years. This means that if we subtract 5 from the present age of the wife and child and take the average, it should be equal to 20.
**Step 2: Set up equations**
Based on the given information, we can set up the following equations:
Equation 1: (H - 3 + W - 3 + C - 3) / 3 = 27
Equation 2: (W - 5 + C - 5) / 2 = 20
Simplifying Equation 1:
(H - 3 + W - 3 + C - 3) / 3 = 27
(H + W + C - 9) / 3 = 27
H + W + C - 9 = 81 (multiplying both sides by 3)
H + W + C = 90
Simplifying Equation 2:
(W - 5 + C - 5) / 2 = 20
(W + C - 10) / 2 = 20
W + C - 10 = 40 (multiplying both sides by 2)
W + C = 50
**Step 3: Solve the equations**
We now have two equations:
H + W + C = 90
W + C = 50
Subtracting the second equation from the first equation, we can find the value of H:
(H + W + C) - (W + C) = 90 - 50
H = 40
Therefore, the present age of the husband is 40 years. Hence, the correct answer is option A.
**Step 1: Understand the given information**
According to the question, 3 years ago, the average age of the husband, wife, and child was 27 years. This means that if we subtract 3 from the present age of each person and take the average, it should be equal to 27.
Similarly, 5 years ago, the average age of the wife and the child was 20 years. This means that if we subtract 5 from the present age of the wife and child and take the average, it should be equal to 20.
**Step 2: Set up equations**
Based on the given information, we can set up the following equations:
Equation 1: (H - 3 + W - 3 + C - 3) / 3 = 27
Equation 2: (W - 5 + C - 5) / 2 = 20
Simplifying Equation 1:
(H - 3 + W - 3 + C - 3) / 3 = 27
(H + W + C - 9) / 3 = 27
H + W + C - 9 = 81 (multiplying both sides by 3)
H + W + C = 90
Simplifying Equation 2:
(W - 5 + C - 5) / 2 = 20
(W + C - 10) / 2 = 20
W + C - 10 = 40 (multiplying both sides by 2)
W + C = 50
**Step 3: Solve the equations**
We now have two equations:
H + W + C = 90
W + C = 50
Subtracting the second equation from the first equation, we can find the value of H:
(H + W + C) - (W + C) = 90 - 50
H = 40
Therefore, the present age of the husband is 40 years. Hence, the correct answer is option A.
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