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### Maths Logic Puzzle

Maths Logic Puzzle - 13 September

There is hypothetical state between india and pakistan border 'paglapur'.
Here 70 percent of the population have defective eyesight, 75 percent are hard of hearing, 80 percent have sinus trouble and 85 percent suffer from allergies, what percentage (at a minimum) suffer from all four ailments?

1. 45 percent

2. max percent - (100 percent - min percent)
= 85-(100-70)
= 55

3. eyesight, 75 percent

4. 10 % is the answer

5. 10%

= (85 + 80 + 75 + 70) - 300 = 10

1. how come 10 ??
from where u get 300 ??

6. 55%
out of 100 the min overlapped area possible between 85(max) and 70(min) is 70-(100-85) or 80-(100-70)

7. 70% * 75% * 80% * 85% = 35.7%

8. 10%
bocoz
70% eyesight ==> 30% ppl no eyesight prob
75% hearing ==> 25% ppl no hearing prob
80% sinus ==> 20% no sinus prob
85% allergies ==> 15% no allergies
To make 100% sure of % of ppl with all problems:
In a number line of 100 ppl if you fill first 30% ppl with no eyesight problem, next 25% ppl with no hearing prob, next 20% with no sinus prob and 15% ppl with no allergies we still left with 10% ppl who will definitely have all the 4 problems. So min. 10% ppl will be definitely there no matter how ever you distribute these problems to those 100 ppl.

As simple as that...:)

9. erza scarlet
i think 10

10. 30% have no eye problem. 75% with hearing problem, so min. 45% (75-30) in them have eye problem too.

Other defects percentage is larger the sharing the other defects will be larger.

So the min. 45% will have all 4 defects.

Nice Problem!

11. In continuation to above: Actually 45% is min. overlap of 70% & 75% (70+75-100) i.e., having both eye & ear problems. 80% have sinus, so the min. overlap of 45% & 80% is 25%. 85% have allergies, so the min. overlap of 25% (having 3 problems) and 85% is (25+85-100) i.e., 10% will have all the four deficiencies.

Now I learnt why directly 70+75+80+85-300=10 is used by some body.

12. 10% is your answer.. let me is thier any one physically fit in that village or not.. Everyone body having different problem...

13. its 10 percent

14. sure 10% {(100-70)+(100-75)+(100-80)+(100-85)}=90
so 90% are free from these 4 decease so the right answer is=(100-90)=10%

1. How can 90% be free of these 4 diseases if 70% have defective eyesight etc etc? That makes no sense.

15. 70% of the population have defective eyesight.

Of that 70% a further 75% of those are hard of hearing.
70% x 75% = 52.5% eyesight and hearing problems

Of that 52.5% a further 80% also have sinus trouble.
So 52.5% x 80% = 42% suffer from eyesight, hearing and sinus problems.

Of that 42% a further 85% also suffer from allergies
42% x 85% = 35.7% suffer from all 4 aliments.

Conversely 0.225% are free from all 4.