Question

10% of garments produced in a mill are found detective and 20% of the remaining are sold in the mills factory outlet. if the remaining 5040 garments are shipped to other retail stores then the garments that were defective was?

Answer 1

AnswEr :

Let the Total Garments produced be n.

• Faulty = 10%
• Perfect = (100 – 10)% = 90%
• 20% of Remaining are Shipped.
• Remains of Remaining Garments = (100 – 20)% = 80% = 5040

$\boxed{\begin{minipage}{5.3 cm}\underline{\qquad\quad\sf n\:(Total)\qquad\quad}\\\quad\swarrow\qquad\qquad\qquad\searrow\\\sf90\%(Perfect)\qquad10\%(Faulty)\\\swarrow\qquad\qquad\searrow\\\sf20\%(Sold)\quad80\%(Remains = 5040)\end{minipage}}$

$\rule{150}{1}$

$\underline{\bigstar\:\textsf{According to the Question Now :}}$

$\longrightarrow\tt Total \times (100-Faulty)\%\times (100 - Sold)\% = 5040\\\\\\\longrightarrow\tt n \times (100 - 10)\% \times(100-20)\%= 5040\\\\\\\longrightarrow\tt n \times 90\%\times80\% = 5040\\\\\\\longrightarrow\tt n \times \dfrac{90}{100}\times\dfrac{80}{100} = 5040\\\\\\\longrightarrow\tt n=5040 \times \dfrac{100}{90}\times\dfrac{100}{80}\\\\\\\longrightarrow\tt n = 70 \times 10\times10\\\\\\\longrightarrow\tt n = 7000$

$\rule{200}{2}$

$\underline{\bigstar\:\textsf{Faulty Garments Produced :}}$

$:\implies\tt Faulty= Total \times Faulty\%\\\\\\:\implies\tt Faulty= n \times 10\%\\\\\\:\implies\tt Faulty=7000 \times \dfrac{10}{100}\\\\\\:\implies\tt Faulty=70\times 10\\\\\\:\implies\boxed{\tt Faulty=700}$

⠀

$\therefore\:\underline{\textsf{Faulty Garments Produced were \textbf{700.}}}$

Answer 2

Answer: 700

Step-by-step explanation:

Let the total number of garments produced be 'x'.

Since it is given that 10% of the garments were found as defective.

Therefore

Defective garment = 10% of x

                               = (10/100) × x

                               = x/10.

Remaining garments = x - x/10

                                   = (10x - x)/10

                                   = 9x/10  

Now, as per given that 20% of  remaining garments are sold in the mills factory.

Garments sold in mill factory =  20% of (9x/10)

                                                   = 20/100 × (9x/10)

                                                   = 9x/50.

Remaining garments are being sold in mills factory is 5040.

Thus we have,

9x/10 - 9x/50 = 5040

(45x - 9x)/50 = 5040

36x/50 = 5040

36x/5 = 5040

36x = 5040 × 50

36x = 252000

x = 252000/36

x = 7000    

Thus,

Defective garments = x/10

                                   = 7000/10

                                   = 700