Question : A mask manufacturing company manufactured an ‘$x$’ number of masks in 2018. It increased its manufacturing capacity by 30% in 2019 and further increased its manufacturing by 15% in 2020. In 2021, due to the machinery breakdown, its manufacturing declined by 40%. What is the value of ‘X’ if it manufactured 179400 masks in 2021?
Option 1: 180000
Option 2: 230000
Option 3: 200000
Option 4: 210000
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Correct Answer: 200000
Solution :
Given: A mask manufacturing company manufactured an ‘$x$’ number of masks in 2018. It increased its manufacturing capacity by 30% in 2019 and further increased its manufacturing by 15% in 2020.
Mask manufactured in 2019 = $x × \frac{130}{100}$ = $\frac{13x}{10}$
Mask manufactured in 2020 = $\frac{13x}{10} × \frac{115}{100}$
Mask manufactured in 2021 = $\frac{13x}{10}×\frac{115}{100}×\frac{100-40}{100}$ = $\frac{13x}{10}×\frac{23}{20}×\frac{3}{5}$
According to the question,
⇒ $\frac{13x}{10}×\frac{23}{20}×\frac{3}{5} = 179400$
⇒ $x = \frac{179400×10×20×5}{13×23×3}$
$\therefore x = 200000$
Hence, the correct answer is 200000.
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