‘N’ men can complete a work together in 24 days. All of them started the work together, but each day, four men left the work. The total time taken to complete the work is now 32 days. Which of the following statement(s) is/are true? 
I. ‘N’ is a multiple of 4 
II. 0.5N + 20 = 0.7N – 22 
III. HCF of (N – 35) and (N + 25) is 40  

Let the efficiency of each man be 1e unit/day. 
Total work = N × 24 × 1e = 24Ne units 
Now, 
N × 1e + (N – 4) × 1e + (N – 8) × 1e + … + (N – 124) × 1e = 24Ne 

Or,  N + (N – 4) + (N – 8) + … + (N – 124) = 24N 

Or,  32N – 4 × (1 + 2 + 3 + … + 31) = 24N 
Or,  8N = 4 × (31 × 32 ÷ 2) 
Or,  8N = 4 × 496 = 1984 
Or,  N = 248 
Statement I: 
248 is a multiple of 4. 
So, Statement I is true. 
Statement II: 
0.5N + 20 = 0.5 × 248 + 20 = 124 + 20 = 144 
0.7N – 22 = 0.7 × 248 – 22 = 173.6 – 22 = 151.6 (not equal) 
So, Statement II is false. 
Statement III: 
N – 35 = 248 – 35 = 213 
N + 25 = 248 + 25 = 273 
HCF of 213 and 273 = 3 
So, Statement III is false. 
Therefore, only Statement I is true.