Question
There are a certain number of tins that are filled with milk from a machine. If the machine fills at the rate of 5 tins/min, 3 tins are left empty; at the rate of 8 tins/min, 5 tins are left empty and and the rate of 7 tins/min, 4 tins are left empty. In this setup it is possible to have N different number of tins. Find N, given that (100<N<1000). There is no leakage or wastage of milk and the machine can work only for integral number of minutes.
Answer: Option C
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C
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C
Option c
Using CRT
5A+3=8B+5
5A=8B+2, B=1 and A=2 .the AP is of the form 40K +13
40K+13=7C+4
7C=40K+9
7c=5K+2 ⇒ K=1 and C=7. The AP is of the form 53+280N
Three digit numbers possible in this AP are 53+280=333 , 53+2(280)=613 and 53+3(280)=893.
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