Discussion

Explanation:

Let the number of people visiting Panchmari alone = x.
From (1): Number of tourists visiting Panchmari and Khajuraho is also x.

Let the number of people visiting all three places = a.

∴ Number of people visiting only Panchmari and Khajuraho = x – a.

From (2): Number of people visiting Khajuraho alone = 2a.

From (4): Number of people visiting Hanumantia alone = 2a – 20.

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From (3 and 5): Number of people visiting Hanumantia alone = 340 – 200 = 140.

⇒ 2a – 20 = 140
⇒ a = 80

Total number of people visiting Madhya Pradesh = 740 = 340 + x + (x – a) + 2a
⇒ 740 = 340 + 2x + a
⇒ 2x + 80 = 400
 ⇒ x = 160

From (5): b + a + c = 200
⇒ b + c = 120   …Eq. (1)

Now, number of people visiting 
Panchmari = 2x + b = 320 + b, and
Khajuraho = 2a + x + c = 320 + c

From (6): 320 + b > 320 + c
⇒ b > c

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∴ Minimum value of b is 61​​​

∴ Minimum number of tourists visiting both Panchmari and Hanumantia, but not Khajuraho = b = 61.

Hence, 61.

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