Three men A, B and C working together can do a work in 17 days. They start the work together and A works for 5 days and takes rest on the sixth day, B works for 5 days and takes rest on the next two days and C works for 8 days and takes rest on the next three days. In how many days will the work be completed ? (A, B, C work at the same rate)  Choose the correct choice from the following choices
A) 24 days  B) 23 days  C) 22 days  D) 21 days  E) 20 days
Total work is 3*17= 
<gadget id="calculator">3*17</gadget>
<output>51</output>
51 units.   A does 5 days of work every 6 days.   B does 5 days of work every 7 days.   C does 8 days of work every 11 days.   Test the options.   In 20 days:   A will do  5*3 + 2= 
<gadget id="calculator"> 5*3 + 2</gadget>
<output>17</output>
17 units (3 complete cycles and 2 days of work).   B will do  5*2+ 5= 
<gadget id="calculator"> 5*2+ 5</gadget>
<output>15</output>
15 units (2 complete cycles, 5 days of work, and 1 day of rest).   C will do  8*1 + 8= 
<gadget id="calculator"> 8*1 + 8</gadget>
<output>16</output>
16 units (1 complete cycle, 8 days of work, and 1 day of rest).   Total= 17 + 15 + 16= 
<gadget id="calculator">17 + 15 + 16</gadget>
<output>48</output>
48 units.   In 21 days:   A will do  5*3 + 3= 
<gadget id="calculator"> 5*3 + 3</gadget>
<output>18</output>
18 units (3 complete cycles and 3 days of work).   B will do  5*3= 
<gadget id="calculator"> 5*3</gadget>
<output>15</output>
15 units (3 complete cycles).   C will do  8*1 + 8= 
<gadget id="calculator"> 8*1 + 8</gadget>
<output>16</output>
16 units (1 complete cycle, 8 days of work, and 2 days of rest).   Total= 18 + 15 + 16= 
<gadget id="calculator">18 + 15 + 16</gadget>
<output>49</output>
49 units.   In 22 days:   A will do  5*3 + 4= 
<gadget id="calculator"> 5*3 + 4</gadget>
<output>19</output>
19 units (3 complete cycles and 4 days of work).   B will do  5*3 + 1= 
<gadget id="calculator"> 5*3 + 1</gadget>
<output>16</output>
16 units (3 complete cycles and 1 day of work).   C will do  8*1 + 8= 
<gadget id="calculator"> 8*1 + 8</gadget>
<output>16</output>
16 units (1 complete cycle, 8 days of work, and 3 days of rest).   Total= 19 + 16 + 16= 
<gadget id="calculator">19 + 16 + 16</gadget>
<output>51</output>
51 units.   Answer: 22 days.
<result>C</result>
Three men A, B and C working together can do a work in 17 days. They start the work together and A works for 5 days and takes rest on the sixth day, B works for 5 days and takes rest on the next two days and C works for 8 days and takes rest on the next three days. In how many days will the work be completed ? (A, B, C work at the same rate)