Question
Download Solution PDFA group of men decided to do a job in 13 days but 9 men left the work after each day. The work, as a result, got completed in 16 days. How many men were initially in the group?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A group of men decided to do a job in 13 days.
Formula used:
Total work = efficiency × time
Sum of n terms = n/2 × [a + l]
Where, n = number of terms;
a = first term; l = last term
Calculation:
Let the number of person in group initially = x
9 men left work after each day.
So it becomes an A.P series.
⇒ x + (x -9) + (x - 18)............ (x - 135) = x × 13
⇒ (16/2) × [x + x - 135] = 13x
⇒ 8 × [2x - 135] = 13x
⇒ 16x - (135 × 8) = 13x
⇒ 16x - 13x = 135 × 8
⇒ x = (135 × 8)/3 = 45 × 8 = 360 persons.
∴ The correct answer is 360 persons.
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