‘N’ men can complete a work together in 24 days. All

Solution

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.