Question

100 million bacteria can completely decompose a garbage dump in 15 days and 60 million
bacteria 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?​

Answer 1

SOLUTION

GIVEN

100 million bacteria can completely decompose a garbage dump in 15 days and 60 million bacteria can do so in 30 days.

Same quantity of garbage is added to the initial quantity of the dump everyday,

TO DETERMINE

The number of bacteria will be required to completely decompose the dump in 10 days

EVALUATION

Let Initially there were x units of garbage and everyday y million of garbage gets added.

Now it is given that 100 million bacteria can completely decompose a garbage dump in 15 days

∴ x + 15y = 1500 - - - - (1)

Again 60 million bacteria can do so in 30 days

∴ x + 30y = 1800 - - - - - (2)

Equation 2 - Equation 1 gives

15y = 300

⇒ y = 20

From Equation 1 we get

x = 1500 - 300 = 1200

Now we have to find the number of bacteria will be required to completely decompose the dump in 10 days

So y = 10

Hence the required number of bacteria will be required to completely decompose the dump in 10 days

$\displaystyle\sf{ = \frac{1200 + (20 \times 10)}{10} \: \: million}$

$\displaystyle\sf{ = \frac{1200 + 200}{10} \: \: million}$

$\displaystyle\sf{ = \frac{1400}{10} \: \: million}$

$\displaystyle\sf{ = 140 \: \: million}$

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