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The hostel cost for 50 children for 8 weeks = rs.1800.
The hostel cost for 1 child for 8 weeks = 1800/50
The hostel cost for 1 child for 1 week = 1800/50 * 8
So, the hostel cost for 90 children for 1 week = (1800 * 90)/(50 * 8)
The cost of keeping 90 children for x number of weeks = Rs. 21060
Thus,
(1800 * 90 * x)/(50 * 8) = 21060
x = (21060 * 50 * 8)/(1800 * 90)
x = 8424000/162000
x = 52
So, the answer is 52 weeks.
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