I'd be interested to see where you got that figure from.
The current figures for those that go into care are nothing like that.
Today, if you are currently aged 65, then you can expect to live to 87.5 on average if you're a woman and 85 if you're a man (source ONS).
Of women aged 80-84 there are 3.9% in care homes, but this does more than double to 8.7% for those aged 85-89.
(the figure does rise dramatically for those aged 90+. The figure is 21%, so if you live past 90 you have a one in five chance of ending up in a care home, but a four out of five chance of not being in a care home)
The comparable figures for men are 2.4% for those aged 80-84 and 4.6% for those aged 85-89. So, only one man in twenty aged 85-89 is in a care home (and the average age of death for men is 83).
(source ONS)
So, take 100 women aged 65. Very few indeed will be in care homes before the age of 80. The ONS figures show that out of these 100 women aged 65 then 2.5 will be in a care home before they get to their 80th birthday.
The ONS says that 76 of them will make it to their 80th birthday. Then 59 will make it to their 85th birthday. So, that's an average of 69.7 women at each year between the ages of 80 and 84.
The figures say that 3.9% of those are in care homes, so that is 2.7 women on average in a care home.
Then from having 59 women alive at the age of 85 this falls to 35.8 by the age of 90 and there is an average of 49.9 women alive between the ages of 85 and 89.
The figures say that 8.7% of those women are in care, so that is 4.3 women.
For the 35.8 women that get to the age of 90 and beyond, the figures say that 21% of them will be in a care home, that is 7.5 women.
So, out of a total of 100 women aged 65 today, the figures suggest that 2.5+2.7+4.3+7.5 = 17 women will go into a care home.
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The similar figures for men are quite a bit lower, partly because many fewer men go into care and also because they don't live as long:
Take 100 men aged 65 today. Of those, 2.3 will go into care homes before they are 80.
67 of them will make it to their 80th birthday and 47 will make it to their 85th birthday.
Of these, 2.4% or 1.4 men are in care.
From those 47 men at age 85, 24.5 will make it to their 90th birthday.
Of these men 4.6%, or 1.7 men, are in care.
For the 24.5 men who make it past 90 then 10.1% or 2.7 men are in care homes.
So, for 100 men aged 65 today then there will be 2.3+1.4+1.7+2.7= 8.1 men who go into care homes.
Overall, for every 100 men who are 65 there are 105 women.
So, combining the mens and womens figures gives an average of 12.7 people out of every 100 who are alive at the age of 65 who will go into care homes.