Question

Lakshmi sold two sarees for rupees 1980 on one she lost 10% while on the other she gained 10% find the gain or loss percent in the whole transaction​

Answer 1

Refer to the attachment....

Answer 2

Solution :

Let the cost price of one saree be Rs.R

Let the cost price of other saree be Rs.M

A/q

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

• S.P. of one saree = Rs.1980
• Gain% = 10%

We know that formula of the gain% :

$\boxed{\bf{Gain\%=\frac{S.P.-C.P.}{C.P.} \times 100\%}}}}$

$\longrightarrow\rm{1\cancel{0}\%=\dfrac{1980-R}{R} \times 10\cancel{0}\%}\\\\\longrightarrow\rm{\%=\dfrac{19800-10R}{R} }\\\\\longrightarrow\rm{R=19800-10R}\\\\\longrightarrow\rm{R+10R=19800}\\\\\longrightarrow\rm{11R=19800}\\\\\longrightarrow\rm{R=\cancel{\dfrac{19800}{11} }}\\\\\longrightarrow\rm{\pink{R=Rs.1800}}$

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

• S.P. of one saree = Rs.1980
• Loss% = 10%

We know that formula of the loss% :

$\boxed{\bf{Loss\%=\frac{C.P.-S.P.}{C.P.} \times 100\%}}}}$

$\longrightarrow\rm{1\cancel{0}\%=\dfrac{M-1980}{M} \times 10\cancel{0}\%}\\\\\longrightarrow\rm{\%=\dfrac{10M-19800}{M} }\\\\\longrightarrow\rm{M=10M-19800}\\\\\longrightarrow\rm{M-10M=-19800}\\\\\longrightarrow\rm{-9M=-19800}\\\\\longrightarrow\rm{M=\cancel{\dfrac{-19800}{-9} }}\\\\\longrightarrow\rm{\pink{M=Rs.2200}}$

Now;

Total Cost price of both sarees = R + M

Total Cost price of both sarees = Rs.1800 + Rs.2200

Total Cost price of both sarees = Rs.4000

&

Total Selling price of both sarees = Rs.1980 + Rs.1980

Total Selling price of both sarees = Rs.3960

∴ C.P. > S.P.

We know that formula of the Loss % :

$\longrightarrow\tt{Loss\%=\dfrac{C.P.-S.P.}{C.P.} \times 100\%}\\\\\\\longrightarrow\tt{Loss\%=\dfrac{4000-3960}{4000} \times 100\%}\\\\\\\longrightarrow\tt{Loss\%=\dfrac{40}{40\cancel{00}} \times \cancel{100}\%}\\\\\\\longrightarrow\tt{Loss\%=\cancel{\bigg(\dfrac{40}{40} \bigg)}\%}\\\\\\\longrightarrow\tt{\pink{Loss\%=1\%}}$

The loss % in the whole transaction will be 1% .