Question

Out of a group of 245 pilgrims, 105 visited Badrinath, 95 visited Kedarnath and 95 visited Somnath. 15 of them visited all the three shrines, while 190 visited exactly one of the three shrines. The number of pilgrims who visited exactly two out of the thre three shhrine is three times as many as those who have not visited any one of the three shrines. How many pilgrims have not visited any one of the three shrines?

Answer 1

There are four possiblities
Pilgrim visited all three shrines=15
" " exactly 2shrines=x
" " " 1 " =190
" " " no shrine=y
Total Pilgrim =245
x=3y or x-3y=0
x+y=245-(190+15)
x+y=40
Solving eqns
x=30
y=10
So ans is 10 pilgrims

Answer 2

10 pilgrims have not visited any of the shrines.

• There are total 245 pilgrims.
• 105 pilgrims visited Badrinath, 95 pilgrims visited Kedarnath and 95 pilgrims visited Somnath. 15 pilgrims visited all of them and 190 pilgrims visited exactly one of the three shrines.
• Now we have to calculate the number pf pilgrims that have not visited any of the pilgrims.
• We have a relation between the number of pilgrims who visited exactly two of the three shrines and those who have not visited any of the shrines.
• Let the number of pilgrims that have visited exactly two of the three shrines be x and the number of people who have not visited any shrines be y.
• Relation is given as ,

x = 3y

x - 3y = 0    (Equation 1)

• Now we need another equation to solve the equation, we obtain by

Total number of pilgrims = sum of pilgrims who visited exactly two shrines , sum of pilgrims who visited none of the shrines  and pilgrims who visited all the three shrines.

245 = (x+y) + 190 + 15

x+y = 40     (Equation 2)

• Solving equations 1 and 2 we get,

Subtracting 2 from 1

-4y = -40

y = 10

• 10 pilgrims have not visited any of the pilgrims.