# Solved Example #10

Monday, February 11th, 2013

Question : 100 million bacteria can completely decompose a garbage dump in 15 days and 60 million can do so in 30 days. If same quantity of garbage is added to the initial quantity of the dump everyday , how many bacteria will be required to completely decompose the dump in 10 days?

Let us say 1 Million bacteria can clear 1 unit of garbage in 1 day.

Initially there were ‘x’ units of garbage and everyday ‘y’ units of garbage gets added.

Case 1 : 100 M bacteria can decompose in 15 days.

Total garbage present = Total garbage decomposed

=> x + 15y = 100*15 …(1)

Case 2 : 60 M bacteria can decompose in 30 days.

=> x + 30y = 100*18 …(2)

Subtract equ(1) from equ(2) to get

15y = 300

=> y = 20 {This means that 20 units of garbage gets added every day}

=> x = 1200 {We got this by putting the value of ‘y’ in equ(1) or equ(2). This means that there was 1200 units of garbage present initially}

Case 3 : We have 10 days to decompose the bacteria

Total garbage = 1200 + 20*10 = 1400 units.

Bacteria required = 1400 / 10 = 140 Million