Question

In 15 days, the earth picks up $1.2 \times {10^8}$ kg of dust from the atmosphere. In how many days it will pick up $4.8 \times {10^8}$ kg of dust?

Answer 1

We will first find out in how many days the earth picks up 1 kg of dust using the data of 15 days. Using this data, we will then find out in how many days does the earth pick $4.8 \times {10^8}$ kg of dust.

Complete step by step answer:
We are given that the earth picks up $1.2 \times {10^8}$ kg of dust from the atmosphere in 15 days.
By unitary method, we know that:-
The earth picks up 1 kg of dust in $\dfrac{{15}}{{1.2 \times {{10}^8}}}$ days.
By simplifying the calculation of number of days, we get:-
$\Rightarrow$ The earth picks up 1 kg of dust in $12.5 \times {10^{ - 8}}$ day.
Now if we multiply both of the sides by $4.8 \times {10^8}$, we will then obtain:-
$\Rightarrow$ The earth picks up $4.8 \times {10^8}$ kg of dust in $12.5 \times {10^{ - 8}} \times 4.8 \times {10^8}$ days.
By simplifying the calculation of number of days, we get:-
$\Rightarrow$ The earth picks up $4.8 \times {10^8}$ kg of dust in 60 days.

Hence, the correct answer is 60 days.

Note: The students must note that if you want to relate it to something easier. You can think of it like, if 5 pens cost you Rs. 10, then how much will 10 pens cost you.
You first find out the cost of 1 pen using the data that 5 pens cost Rs. 10.
Now, using this data, we find the cost of 10 pens.
The students must note that, they can make the same question even more brief by not using so many step and doing this in fewer like as follows:-
The earth picks up $1.2 \times {10^8}$ kg of dust from the atmosphere in 15 days.
The earth picks up $4.8 \times {10^8}$ kg of dust from the atmosphere in $\dfrac{{15 \times 4.8 \times {{10}^8}}}{{1.2 \times {{10}^8}}}$ days.
Simplifying the calculations, we will get:-
The earth picks up $4.8 \times {10^8}$ kg of dust from the atmosphere in $15 \times 4$ days.
Simplifying the calculations further, we will get:-
The earth picks up $4.8 \times {10^8}$ kg of dust from the atmosphere in 60 days.