Question

A man spends 20% of his salary on house rent. After spending 25% of the remainder
he has Rs 4800 left. What is his monthly salary?
After allowing a discount of 25% on a sweater, it is sold for Rs. 720. Find its marked​

Answer 1

Question 1 :

Let the Monthly Salary of Man be Rs. n

$\boxed{\begin{minipage}{6 cm}\underline{\qquad\quad\sf Rs.\:n\:(Salary)\qquad\quad}\\\quad\swarrow\qquad\qquad\qquad\searrow\\\sf80\%(Remains)\qquad20\%(Rent)\\\swarrow\qquad\qquad\searrow\\\sf25\%(Spend)\quad75\%(Remains = Rs.\:4800)\end{minipage}}$

$\rule{150}{1}$

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

$\longrightarrow\tt Total \times (100-Salary)\%\times (100 - Spend)\% = 4800\\\\\\\longrightarrow\tt n \times (100 - 20)\% \times(100-25)\%= 4800\\\\\\\longrightarrow\tt n \times 80\%\times75\% = 4800\\\\\\\longrightarrow\tt n \times \dfrac{80}{100}\times\dfrac{75}{100} = 4800\\\\\\\longrightarrow\tt n=4800 \times \dfrac{100}{80}\times\dfrac{100}{75}\\\\\\\longrightarrow\tt n = 4800 \times \dfrac{5\times4}{4\times3}\\\\\\\longrightarrow\tt n =400 \times 20\\\\\\\longrightarrow \boxed{\tt n = Rs. \:8000}$

⠀

$\therefore\:\underline{\textsf{Monthly Salary of Man is \textbf{Rs. 8000}}}$

$\rule{250}{2}$

Question 2 :

$\bf{ Given}\begin{cases}\sf{Discount\% = 25\%}\\\sf{SP = Rs. \:720}\\ \sf{MP = \: ?}\end{cases}$

$\rule{150}{1}$

$\underline{\bigstar\:\textsf{Calculation of Marked Price :}}$

$\longrightarrow\tt SP = MP \times (100-Discount)\%\\\\\\\longrightarrow\tt 720 = MP \times (100-25)\%\\\\\\\longrightarrow\tt 720 = MP \times 75\%\\\\\\\longrightarrow\tt 720 = MP \times \dfrac{75}{100}\\\\\\\longrightarrow\tt 720 = MP \times \dfrac{3}{4}\\\\\\\longrightarrow\tt 720 \times \dfrac{4}{3}=MP\\\\\\\longrightarrow\tt 240 \times 4=MP\\\\\\\longrightarrow\boxed{\tt MP = Rs. \:960}$

⠀

$\therefore\:\underline{\textsf{Marked Price of Sweater is \textbf{Rs. 960}}}$

Answer 2

$\bold\red{Monthly\:salary }$ = $\bold{Rs.8000}$

$\bold\green{Marked\:price }$ = $\bold{Rs.960}$

Step-by-step explanation:

$\bold{1st\:case:-}$

$\bf{Given}\begin{cases}\sf {Spending\:on\:house\:rent = 20\%}\\\sf{Spending\:on\:remainder = 25\%}\\\sf{Left = Rs.4800}\\\sf{Monthly\:salary=?}\end{cases}$

Let monthly salary be Rs. X

At first,

$\mapsto\sf Monthly\:salary \times 20\% \\\\\mapsto\sf X \times 20\% = X \times \dfrac{20}{100} \\\\\mapsto\sf \dfrac{20X}{100} \\\\\mapsto\sf \dfrac{X}{5}$

$\rule{300}{1}$

$\mapsto\sf MS - MS \times 20\% \\\\\mapsto\sf X - \dfrac{X}{5} \\\\\mapsto\sf \dfrac{5X - X }{5} \\\\\mapsto{\boxed{\sf \red{\dfrac{4X }{5}.........(i)}}}$

$\rule{300}{1}$

$\mapsto\sf \dfrac{4X}{5}\times 25\% \\\\\mapsto\sf \dfrac{4X}{5} \times \dfrac{25}{100} \\\\\mapsto\sf \dfrac{4X}{5}\times \dfrac{1}{4} \\\\\mapsto{\boxed{\sf\red{ \dfrac{4X}{20}..........(ii)}}}$

${\underline{\underline{\bold{According\:to\:question:-}}}}$

$\mapsto\sf \dfrac{4X}{5} - \dfrac{4X}{20} = 4800 \\\\\mapsto\sf \dfrac{16X - 4X}{20}= 4800 \\\\\mapsto\sf 12X = 96000 \\\\\mapsto\sf X =\dfrac{96000}{12} \\\\\mapsto{\boxed{\sf\red{X = 8000}}}$

$\therefore\bold{Monthly\:salary = Rs.8000}$

$\rule{300}{1}$

$\bold{2nd\:case:-}$

Given:-

• SP = Rs.720
• Discount = 25%
• Marked price = ?

We know that,

$\bigstar{\boxed{\bold{Selling \:price = Marked \:price - Marked\:price\times Discount\%}}}$

$\mapsto\sf 720 = MP - MP \times 25\% \\\\\mapsto\sf 720 = MP - MP \times \dfrac{25}{100} \\\\\mapsto\sf 720 = MP - \dfrac{MP}{4} \\\\\mapsto\sf 720 = \dfrac{4MP - MP }{4}\\\\\mapsto\sf 720 \times 4 = 3MP \\\\\mapsto \sf 2880 = 3MP \\\\\mapsto\sf MP =\dfrac{2880}{3}\\\\\mapsto{\boxed{\sf{ MP = Rs.960 }}}$

$\therefore\bold{Marked\:price = Rs.960}$