Aman, Bharat, Eman, Chandan, Deepak, Fakir, Gopal and Hari were buying apples. One variety was Rs 10 for 11 and other Rs 5 for 7. Four apples were stolen and the seller later realised and asked them to count the number of apples they were carrying. It was found that Aman had 33, Bharat 32, Chandan 78, Deepak 35, Eman 37, Fakir 36, Gopal 39 and Hari 34. Who seems to have the apples not paid for ?
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We write the number of apples for each n group of 11 and 7:
Aman: 0 x 7 + 3 x 11 = 33 Bharat: 3 x 7 + 1 x 11 = 32 Chandan: 8 x 7 + 2 x 11 =78 Deepak: 5 x 7 + 0 x 11 = 35 Eman: (5 x 7 + 0 x 11) + 2 = 37 (2 apples unpaid) Fakir: 2 x 7+2 x 11 = 36' Gopal: 4 x 7+1 x 11 =39 Hari: (3 x 7 + 1 x 11) + 2 = 34 (2 apples unpaid)
So Eman and Hari