self Maths Puzzle Numerical Ability Time and Work

A painting job can be completed by 8 painters in 17 days. If 8 more painters join the team 3 days after starting work on the job, then how many more days are required to complete the job?

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Ans 7 DAYS
8 painter 1 day job=1/17, Therefore 8 painter 3 days job=3/17
Remaining job=1-3/17=14/17
If for remaining job 8 more painter joins
The 1 day job of (8+8) painter =2/17
Days require for completion of remaining job of 14/17=(14/17)*(17/2)= 7 Days
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self Other Question

Your teacher has a total of 36 chalks. When a chalk reduces to 1/6 of its original size, it gets too small for her to hold for writing and hence she keeps it aside. But your teacher hates wasting things and so, when she realizes that she has enough of these small pieces to join and make another chalk of the same size, she joins them and uses the new chalkstick. If she uses one chalk each day, how many days would the 36 chalks last? Can you find a quick and elegant way to add the numbers from 1 to 34 ?

In other words, what is the sum you obtain in the following case:

1 + 2 + 3 + ....... + 34 =