Question

A man sold two mobile set for Rs 2400 each gaining 20 percent in first set and loosing 20 percent on the other ,Find his net profit or loss as percent of the whole ,with rough work​

Answer 1

Solution :

$\bf{\red{\large{\underline{\bf{Given\::}}}}}$

A man sold two mobile set for Rs.2400 each gaining 20% in first set and loosing 20% on the other.

$\bf{\red{\large{\underline{\bf{To\:find\::}}}}}$

The net profit or loss percent of the whole transaction.

$\bf{\red{\large{\underline{\bf{Explanation\::}}}}}$

Let the 1st mobile of Cost price be Rs.R

Let the 2nd mobile of Cost price be Rs.M

$\underbrace{\tt{1_{st}\:Case\::}}}}$

$\bf{We\:have}\begin{cases}\sf{Cost\:price\:(C.P.)_{1}=Rs.R}\\ \sf{Selling\:price\:(S.P.)_{1}=Rs.2400}\\ \sf{Profit\:(\%)=20\%}\end{cases}}$

Therefore;

$\longrightarrow\sf{Gain(\%)=\bigg(\dfrac{(S.P.)_{1}-(C.P.)_{1}}{(C.P.)_{1}} \bigg)\times 100\%}\\\\\\\longrightarrow\sf{2\cancel{0}\%=\bigg(\dfrac{2400-R}{R} \bigg)\times 10\cancel{0}\%}\\\\\\\longrightarrow\sf{2=\dfrac{24000-10R}{R} }\\\\\\\longrightarrow\sf{2R=24000-10R}\\\\\\\longrightarrow\sf{2R+10R=24000}\\\\\\\longrightarrow\sf{12R=24000}\\\\\\\longrightarrow\sf{R=\cancel{\dfrac{24000}{12} }}\\\\\\\longrightarrow\sf{\orange{R=Rs.2000}}$

$\underbrace{\tt{2_{nd}\:Case\::}}}}$

$\bf{We\:have}\begin{cases}\sf{Cost\:price\:(C.P.)_{2}=Rs.M}\\ \sf{Selling\:price\:(S.P.)_{2}=Rs.2400}\\ \sf{Loss\:(\%)=20\%}\end{cases}}$

Therefore;

$\longrightarrow\sf{Loss(\%)=\bigg(\dfrac{(C.P.)_{2}-(S.P.)_{2}}{(C.P.)_{2}} \bigg)\times 100\%}\\\\\\\longrightarrow\sf{2\cancel{0}\%=\bigg(\dfrac{M-2400}{M} \bigg)\times 10\cancel{0}\%}\\\\\\\longrightarrow\sf{2=\dfrac{10M-24000}{M} }\\\\\\\longrightarrow\sf{2M=10M-24000}\\\\\\\longrightarrow\sf{2M-10M=-24000}\\\\\\\longrightarrow\sf{-8M=-24000}\\\\\\\longrightarrow\sf{M=\cancel{\dfrac{-24000}{-8} }}\\\\\\\longrightarrow\sf{\orange{M=Rs.3000}}$

Thus;

Total Cost price of both Mobile set = R + M = Rs.(2000+3000) = Rs.5000

Total Selling price of both Mobile set = Rs.4800

A/q

C.P. > S.P.

$\mapsto\sf{Loss\:(\%)=\bigg(\dfrac{C.P.-S.P.}{C.P.} \bigg)\times 100\%}\\\\\\\mapsto\sf{Loss\:(\%)=\bigg(\dfrac{5000-4800}{5000}\bigg)\times 100\%} \\\\\\\mapsto\sf{Loss\:(\%)=\dfrac{200}{50\cancel{00}} \times \cancel{100}\%}\\\\\\\mapsto\sf{Loss\:(\%)=\cancel{\bigg(\dfrac{200}{50} \bigg)}\%}\\\\\\\mapsto\sf{\orange{Loss\:(\%)=4\:\%}}$

Thus;

$\underline{\sf{The\:loss\:percent\:of\:the\:whole\:transaction\:is\:\:4\%}}}}}$

Answer 2

$\tt{\huge{\orange{Hello!!! }}} M.V$

QUESTION :

A man sold two mobile set for Rs 2400 each gaining 20 percent in first set and loosing 20 percent on the other ,

Find his net profit or loss as percent of the whole ,with rough work.

SOLUTION :

SET 1 :

He gained 20% by selling at a price of Rs. 2400

=> Original Price : x

=> 120/100 x = 2400

=> 2000

So CP 1 = Rs. 2000

SET 2 :

He lost 20% by selling for RS. 2400

=> Original Price : Y

=> 80/ 100 Y = 2400

=> Y = 3000

So Cp 2 = Rs. 3000

Total CP = Rs. 2000 + Rs. 3000 = Rs. 5000

Total SP = Rs. 2400 × 2 = Rs. 4800

Loss = Total CP - Total SP = Rs. 200

Loss Percentage = ( 200 / 5000) × 100 % = 4 %

A n S W e r :

The loss Percentage is 4 %.