Question

5. Out of the total production of Aluminum from
Bauxite, an ore of Aluminum, 30% of the ore gets
wasted, and out of the remaining ore, only 30% is
pure Aluminum. If the pure Aluminum obtained in
a year from a mine of Bauxite was 42,000 kg, then
the quantity of Bauxite mined from that mine in the
year is​

Answer 1

Step-by-step explanation:

let's assume the total production is 100 then,

30% of the ore gets wasted that means,

100x30/100= 70

out of the remaining ore, only 30% is pure aluminum

now,

100x70/100x30/100=42000kg

(100x0.7x0.3)=42000kg

21%= 42000kg

21/100=42000kg

42000x100/21= 200000kg

Answer 2

The quantity of Bauxite mined from that mine in the year is 200000 kg

Given :

• Out of the total production of Aluminum from Bauxite, an ore of Aluminum, 30% of the ore gets wasted, and out of the remaining ore, only 30% is pure Aluminum.

• The pure Aluminum obtained in a year from a mine of Bauxite was 42,000 kg

To find :

The quantity of Bauxite mined from that mine in the year

Solution :

Step 1 of 2 :

Form the equation to find the quantity of Bauxite mined from that mine in the year

Let the quantity of Bauxite mined from that mine in the year = 100q kg

Since out of the total production of Aluminum from Bauxite, an ore of Aluminum, 30% of the ore gets wasted

∴ The percentage of remaining ore

= (100 - 30)%

= 70%

∴ The quantity of remaining ore

$\displaystyle \sf = 100q \times \frac{70}{100} \: \: kg$

$\displaystyle \sf = 70q \: \: kg$

Again out of the remaining ore, only 30% is pure Aluminum.

∴ The quantity of pure Aluminum

$\displaystyle \sf = 70q \times \frac{30}{100} \: \: kg$

$\displaystyle \sf = 21q \: \: kg$

The pure Aluminum obtained in a year from a mine of Bauxite was 42,000 kg

So by the given condition

$\displaystyle \sf 21q = 42000$

Step 2 of 2 :

Calculate the quantity of Bauxite mined from that mine in the year

$\displaystyle \sf 21q = 42000$

$\displaystyle \sf{ \implies }q = \frac{42000}{21}$

$\displaystyle \sf{ \implies }q = 2000$

Hence quantity of Bauxite mined from that mine in the year

= 100q kg

= (100 × 2000) kg

= 200000 kg

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