Discussion

Explanation:

Number of people liking
TOI = 90% of 50,000 = 45,000
ET = 85% of 50,000 = 42,500
HT = 80% of 50,000 = 40,000
MM = 82% of 50,000 = 41,000
DNA = 75% of 50,000 = 37,500
None of the newspapers = 4,000

Let the number of people liking
exactly 1 of these newspapers = a
exactly 2 of these newspapers = b
exactly 3 of these newspapers = c
exactly 4 of these newspapers = d
exactly 5 of these newspapers = e
none of these newspapers = n = 4,000

⇒ a + b + c + d + e + n = 50,000
⇒ a + b + c + d + e = 46,000   ...(1)

Also, a + 2b + 3c + 4d + 5e = 45000 + 42500 + 40000 + 41000 + 37500
⇒ a + 2b + 3c + 4d + 5e = 2,06,000   ...(2)

We need to minimise e. Let us check if e can be 0 or not.
From (1), maximum possible value of d = 46000. Assuming d = 46000, then a = b = c = e = 0
⇒ a + 2b + 3c + 4d + 5e = 1,84,000

Since, we need to increase this sum from 1,84,000 to 2,06,000,
we will have to decrease the value of d and increase the value of variable with highest coefficient i.e., e.

If d = 45,999, e = 1, then the sum will become 1,84,001
i.e., for transfer of 1 unit from 'd' to 'e', sum increases by 1 unit.

We need to increase the sum by 22,000 units.
∴ We need to transfer 22,000 units from 'd' to 'e'.

⇒ Least possible value of e = 22,000

Hence, option (c).

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