Math, asked by sneha4442, 5 months ago

Lakshmi sold to Sari for 1980 each .on one, she lost 10 percent. while on the other she gained 10 percent.find her gain or loss percent in the whole transaction.

Answers

Answered by REONICKSTAR
3

{ \red{ \tt{ \underline{ \purple{ \underline{Given  \: data}}}}}:-}

◐ Lakshmi sold to Sari for 1980 each.

◐ On one, she lost 10 percent.

◐ On the other she gained 10 percent.

{ \red{ \tt{ \underline{ \purple{ \underline{Solution}}}}}:-}

๏ Gain/Profit percent = 10 %

๏ Loss percent = 10 %

Here, C.P is cost price & S.P is selling price.

๏ Selling price ( S.P ) = 1980

→ Profit = S.P - C.P

→ Loss = C.P - S.P

Let, cost price ( C.P ) of first sari be x and

cost price

( C.P ) of second sari be y.

Now, for first sari

{ \tt{ \small{ \dashrightarrow{Profit \:  percent = \frac{(S.P - C.P )}{C.P}  \times 100 }}}}

{ \tt{{ \dashrightarrow{10 = \frac{1980 \:  -  \: x }{x}  \times 100 }}}}

{ \tt{{ \dashrightarrow{10 = \frac{198000 \:  -  \: 100x }{x}   }}}}

{ \tt{{ \dashrightarrow{10x = 198000 \:  -  \: 100x    }}}}

{ \tt{{ \dashrightarrow{10x + 100 x= 198000    }}}}

{ \tt{{ \dashrightarrow{110x= 198000    }}}}

{ \tt{{ \dashrightarrow{ x=  \frac{198000}{110}     }}}}

{ \tt{{ \dashrightarrow{ x=  1800}}}}

Now for second sari

{ \tt{ \small{ \dashrightarrow{Loss \:  percent = \frac{( C.P - S.P )}{C.P}  \times 100 }}}}

{ \tt{ \small{ \dashrightarrow{10 = \frac{ y \:  -  \: 1980 }{y}  \times 100 }}}}

{ \tt{ \small{ \dashrightarrow{10 = \frac{100 y \:  -  \: 198000 }{y}   }}}}

{ \tt{ \small{ \dashrightarrow{10y= 100 y \:  -  \: 198000   }}}}

{ \tt{ \small{ \dashrightarrow{10y - 100 y   =  -  \: 198000   }}}}

{ \tt{ \small{ \dashrightarrow{ - 90 y   =  -  \: 198000   }}}}

{ \tt{ \small{ \dashrightarrow{ y   =  \frac{ - 198000}{ - 90}    }}}}

{ \tt{ \small{ \dashrightarrow{ y   =  2200  }}}}

→ Total cost price of both sari

= x + y

→ Total cost price of both sari

= 1800 + 2200

→ Total cost price of both sari

= 4000 .... ( 1 )

Here, we know, Lakshmi sold to Sari for 1980 each.

Hence,

→ Total selling price of both sari

= 1980 + 1980

→ Total selling price of both sari

= 3960 .... ( 2 )

{from ( 1 ) & ( 2 )}

→ Cost price is greater than selling price, hence, is in loss, so now

→ Loss = C.P - S.P

→ Loss = 4000 - 3960

→ Loss = 40

{ \tt{ \small{ \dashrightarrow{Loss \:  percent = \frac{Loss}{C.P}  \times 100 }}}}

{ \tt{ \small{ \dashrightarrow{Loss \:  percent = \frac{40}{4000}  \times 100 }}}}

{ \tt{ \small{ \dashrightarrow{Loss \:  percent = \frac{1}{ \cancel{100}}  \times { \cancel{100}} }}}}

{ \tt{ \small{ \dashrightarrow{Loss \:  percent = \: 1 \: percent}}}}

Hence, Lakshmi's loss percent in the whole transaction is 1% .

Similar questions