Correct Answer  Option 1 : 20
The total work (in man days) is (22 × 70) = 1540 man days.
Days

Number of persons

Work done in man days

1

1

1

2

2

1 + 2

3

3

1 + 2 + 3

4

4

1 + 2 + 3 + 4







N

N

(1 + 2 + 3 + 4 +  + N)

Therefore, on the Nth day the work done is (1 + 2 + 3 +  + N) = N(N + 1)/2
If we denote the work done on the N^{th} day by tn.
⇒ tn = N(N + 1)/2
∴ Total work done in N days = t_{1} + t_{2} + t_{3} +  t_{N}
⇒ ∑ N(N + 1)/2
⇒ ∑ N^{2}/2 + ∑N/2
⇒ N (N + 1) (2N + 1)/12 + N (N + 1)/4
⇒ N (N + 1) [(2N + 1 + 3)/12
⇒ N (N + 1) (N + 2)/6
We need to find a value of N, such that N (N + 1) (N + 1)/6 ≥ 1540
⇒ N (N + 1) (N + 2) ≥ (6 × 1540)
⇒ N (N + 1) (N + 2) ≥ 6 × 10 × 7 × 22
⇒ N (N + 1) (N + 2) ≥ (20 × 21 × 22)
∴ N = 20
Therefore, the work gets completed in 20 days.