Correct Answer - Option 1 : NL/1000C

__Explanation:__

Cutting speed in a shaper is the average linear speed of the tool (m/min) during the cutting stroke. It depends on the number of ram strokes per minute and the stroke length.

Cutting speed of shaper is given by;

\(V = \frac{{{\rm{NL\;}}\left( {1{\rm{\;}} + {\rm{\;m}}} \right)}}{{1000}}\;m/min\)

where

V = Cutting speed of shaper, N = Number of double stroke per minute, L = length of stroke

m = Quick return ratio = \(\frac{{{\rm{Time\;of\;return\;stroke}}}}{{{\rm{Time\;of\;cutting\;stroke}}}}\)

**Given**:

\(C=\frac{{Cutting~time}}{{Total~time}}=\frac{{Cutting~time}}{{Return~time\;+\;Cutting~time}}\)

\(\frac{{1}}{{C}}=\frac{{Cutting~time\;+\;Return~time}}{{Cuttting~time}}=1+m\)

\(\therefore V = \frac{{{\rm{NL\;}}\left( {1{\rm{\;}} + {\rm{\;m}}} \right)}}{{1000}}=\frac{{NL}}{{1000C}}\) m/min.