The Solution

If the number of boys who were given marbles is n and the number of marbles each was given was m, the total must have been mn.

Anil was given 1 and a tenth of what remained = 1 + (mn – 1)/10 = (mn + 9)/10

What remained after Anil was given his share is mn – (mn + 9)/10 = (9mn – 9)/10.

Brij was given 2 and a tenth of what remained = 2 + . { (9mn – 9)/10 – 2}/10 = . (9mn + 171)/100.

As Anil and Brij had an equal number, (mn + 9)/10 = (9mn + 171)/100 or mn = 81. 

Thus Anil was given 1 + 80/10 = 9. Hence m = 9. Therefore n = 9.

The last boy’s name should begin with the 9th letter of the alphabet, that is, I and hence must be Indra.

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