Correct Answer - Option 1 : 140
Given:
A group of men decided to construct a wall in 4 days.
Formula:
The sum of n terms of AP is the sum(addition) of first n terms of the arithmetic sequence is:
Sum of n terms of AP = n/2[2a + (n – 1)d]
Where “a” is the first term of the AP series and “d” is the common difference between the second and first term-
Concept:
Total work = Total number of men × Total number of days taken to complete the work.
Calculation:
Let the initial number of men be “m”
According to the concept used,
Total work = 4 m
Again, it is given that 20 men dropped out every day, we can write
m + (m – 20) + (m – 40) + (m – 60) + (m – 80) + (m – 100) + (m – 120) = 4 m
According to the formula used,
if 7 is the total number of days taken and common difference is 20, then the sum of total work can be written as,
⇒ (7/2) × [2m + 6(-20)] = 4 m
⇒ (7/2) × [2m - 120] = 4 m
⇒ 7m - 420 = 4 m
⇒ m = 140
∴ The total number of men who initially decided to construct the wall, if it was completed in 7 days is 140.
