Maths question HELP !!!?

2018-06-28 12:32 am
Few years back when a couple got married, wife was 5 years older than her husband . However, 20 years back , the wife was twice as old as her husband. How old is the wife now?
(a) 20 years
(b) 24 years
(c) 25 years
(d) 30 years
(e) Cannot be determined

回答 (5)

2018-06-28 2:35 am
✔ 最佳答案
Let w be the wife's current age and h be the husband's current age.

20 years back , the wife was twice as old as her husband :
(w-20)/(h-20) = 2

Few (an unknown number of) years back ..., wife was 5 years older than her husband:
No matter how many years back (or forward), the wife will always be 5 years older than her husband since they both age at the same rate..
h = w-5

(w-20)/(w-25) = 2
w - 20 = 2w - 50
w - 2w = 20 - 50
w = 30

The correct answer is that the wife's current age is 30, her husband is 25.

However, to arrive at that solution, you must enforce a third condition such as the condition that both persons age at the same rate. This is a physically reasonable assumption since there is no indication that either of them is moving at a significant percentage of the speed of light relative to the other or that they reside in significantly different gravitational or acceleration fields.
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20 years ago, she was 10 which is twice her husband's age of 5.

The "correct answer is (e)" from your comment to billrussell42's answer is probably because the problem statement provides 3 unknowns but only two equations. That is called an "underdetermined" system which will not have a unique solution. However, you also have the unstated condition that the two persons age at the same rate so the difference in their ages is always 5 years regardless of the number of years back. That gives you the third equation/condition required for the system to converge to a deterministic system with a unique solution.
2018-06-28 12:53 am
Let y years be the age of the wife now.
Then, age of the husband = (y - 5) years now.

20 years back :
y - 20 = [(y - 5) - 20] * 2
y - 20 = 2y - 50
y = 30

The answer: (d) 30 years
2018-06-28 1:25 am
w - 20 = 2(h - 20)
w = h + 5

h = 25, w = 30
n years ago, they were 25 and 30.

Now, they are 25 + n, and 30 + n
2018-06-28 1:16 am
(c)
w = h + 5
w - 20 = 2(h - 20)
h + 5 - 20 = 2(h - 20)
h - 15 = 2h - 40
2h - h = 40 - 15
h = 25
w = 25 + 5 = 30
2018-06-28 12:45 am
let me try few = 2
two years ago wife was 5 years older than her husband
w–2 = h–2+5
w = h + 5

20 years ago
w = 2h
w = h + 5
2h = h + 5
h = 5
w = 10

present, add 20
h = 25
w = 30

ok


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