10 men can do a piece of work in 65 days. If 1 man starts work and the next day 3 men joined him again the next day 5 men joined the group and next day 7 men joined the group and follow the same pattern, now find out in how many days the work will be completed?
10 men can do a piece of work in 65 days. If 1 man starts work and the next day 3 men joined him again the next day 5 men joined the group and next day 7 men joined the group and follow the same pattern, now find out in how many days the work will be completed? Correct Answer 12 days
Given:
10 men can do the work in 65 days.
And 1 man started the work and the next day 3 men joined and the next day 5 men joined and the pattern followed like this.
Concept:
We will find how many people work every day then solve the question.
Formula used:
Sum of squares of N natural numbers number = N(N + 1)(2N + 1)/6
Calculation:
If 10 man can do the work in 65 days
⇒ 1 man can do the same work in 650 days
⇒ From here we get the efficiency of 1 man is 1 unit
Now 1st day 1 man, 2nd day (1+3) = 4 men, next day (4 + 5) = 9 men
Now we know the pattern so let the work be performed in N days
N day work = 650 units
⇒ 1 + 4 + 9 + 16 + ……….. n days = 650
⇒ N (N +1)(2N + 1)/6 = 650
⇒ N (N + 1)(2N + 1) = 650 × 6
∴ From options we get N = 12 days
