In a battle, 70% of the combatants lost one eye, 80% lost one leg, 85% lost ear, 90% an arm. If x% lost all the four organs, then minimum value of x is

Q: In a battle, 70% of the combatants lost one eye, 80% lost one leg, 85% lost ear, 90% an arm. If x% lost all the four organs, then minimum value of x is

Ans:
Let,
70% of the combatants who lost one eye = A
80% of the combatants who lost one leg = B
85% of the combatants who lost ear = C
90% of the combatants who an arm = D

Then,
The combatants who lost one eye and one leg
n(A∩B) =  n(A) + n(B) - n(AUB)
⇒n(A∩B) = 70% +80% - 100%
⇒n(A∩B) 50%

Similarly we can find out as follows:
The combatants who lost one leg and one ear = 65%
The combatants who lost one ear and one arm = 75%
The combatants who lost one arm and one eye = 60%

Using
n(AUBUCUD) =  n(A) + n(B) + n(C) + n(D) -n(A∩B) -n(B∩C) - n(C∩D) - n(A∩D) + n(A∩B∩C∩D)

⇒n(A∩B∩C∩D) =  n(AUBUCUD) - n(A) -  n(B) - n(C) - n(D) + n(A∩B) + n(B∩C) + n(CND) + n(A∩D)

⇒n(A∩B∩C∩D) = 100% - 70 % - 80% - 85% - 90% + 50% + 65% + 75% + 60%

⇒n(A∩B∩C∩D) = 25%

∴ The value of x is 25