Question

3.
Ankit sold two jeans for 990 each. On one he gains 10% and on the other he lost
10%. Find his gain or loss per cent in the whole transaction.​

Answer 1

AnswEr :

$\bf{Jeans_1}\begin{cases}\sf{Selling \:Price (SP)=Rs. \:990}\\\sf{Gain\%=10\%}\end{cases}$

• Cost Price of First Jeans :

$\longrightarrow \tt SP = CP \times (100 + Gain)\% \\ \\\longrightarrow \tt 990 = CP \times (100 + 10)\% \\ \\\longrightarrow \tt 990 = CP \times 110\% \\ \\\longrightarrow \tt 990 = CP \times \dfrac{110}{100} \\ \\\longrightarrow \tt \cancel{990} \times \dfrac{100}{ \cancel{110}} = CP \\ \\\longrightarrow \tt 9 \times 100= CP \\ \\\longrightarrow \blue{\tt CP = Rs.\:900}$

$\rule{300}{1}$

$\bf{Jeans_2}\begin{cases}\sf{Selling \:Price (SP)=Rs. \:990}\\\sf{Loss\%=10\%}\end{cases}$

• Cost Price of Second Jeans :

$\longrightarrow \tt SP = CP \times (100 - Loss)\% \\ \\\longrightarrow \tt 990 = CP \times (100 - 10)\% \\ \\\longrightarrow \tt 990 = CP \times 90\% \\ \\\longrightarrow \tt 990 = CP \times \dfrac{90}{100} \\ \\\longrightarrow \tt \cancel{990} \times \dfrac{100}{ \cancel{90}} = CP \\ \\\longrightarrow \tt 11 \times 100= CP \\ \\\longrightarrow \blue{\tt CP = Rs.\:1100}$

$\rule{300}{2}$

◗ Total SP = Rs.(990 + 990) = Rs. 1980

◗ Total CP = Rs.(900 + 1100) = Rs. 2000

As, Cost Price ( CP ) is more than Selling Price ( SP ), therefore it will be Loss.

$\implies \tt Loss\% = \dfrac{Loss}{CP} \times 100 \\ \\\implies \tt Loss\% = \dfrac{CP-SP}{CP} \times 100 \\ \\\implies \tt Loss\% = \dfrac{2000 - 1980}{20 \cancel{00}} \times \cancel{100} \\\\\implies \tt Loss\% = \cancel\dfrac{20}{20}\\ \\\implies \large\boxed{\pink{\tt Loss\% =1\%}}$

⠀

∴ Loss% on whole transaction will be 1%

$\rule{300}{3}$

$\boxed{\begin{minipage}{7 cm}\underline{\text{Some Important Formulae Related to it :}}\\ \\ SP=CP\times(100+\sf Profit)\%\\ \\SP=CP\times(100-Loss)\%\\ \\Profit\%=\dfrac{Profit}{CP}\times100 \\ \\Loss\%=\dfrac{Loss}{CP}\times100\end{minipage}}$

#answerwithquality #BAL

Answer 2

$\bf{\Huge{\underline{\boxed{\bf{\pink{ANSWER\::}}}}}}$

$\bf{\Large{\underline{\sf{\purple{Given\::}}}}}$

Ankit sold two jeans for Rs.990 each. On one he gains 10% & on the other he lost 10%.

$\bf{\Large{\underline{\sf{\red{To\:find\::}}}}}$

The loss or gain percent in the whole transaction.

$\bf{\Large{\underline{\sf{\green{Explanation\::}}}}}$

Ankit sold two jeans for Rs.990.

• $\bf{\huge{\underline{\sf{\orange{For\:1st\:Jeans\::}}}}}$

$\bf{We\:have\begin{cases}\sf{Selling\:price\:of\:jeans,[S.P.]=Rs.990}\\ \sf{Gain\:of\:one\:jeans,[profit]=10\%}\\ \sf{Cost\:price,[C.P]=?}\end{cases}}$

We know that formula of the cost price to get gain percent:

→ $\bf{C.P.=\frac{100}{100+profit\%} *S.P.}$

→ $\bf{C.P.=\frac{100}{100+10} *990}$

→ $\bf{C.P.=\frac{100}{\cancel{110}} *\cancel{990}}$

→ C.P. = Rs.(100×9)

→ C.P. = Rs.900

• $\bf{\huge{\underline{\sf{\orange{For\:2nd\:Jeans\::}}}}}$

$\bf{We\:have\begin{cases}\sf{Selling\:price\:of\:jeans,[S.P.]=Rs.990}\\ \sf{loss\:of\:one\:jeans,[loss]=10\%}\\ \sf{Cost\:price,[C.P]=?}\end{cases}}$

We know that formula of the cost price to get loss percent:

→ $\bf{C.P.=\frac{100}{100-loss\%} *S.P.}$

→ $\bf{C.P.=\frac{100}{100-10} *990}$

→ $\bf{C.P.=\frac{100}{\cancel{90}} *\cancel{990}}$

→ C.P. = Rs.(100 × 11)

→ C.P. = Rs.1100

• Total Cost Price of both jeans:

→ First jeans, Rs.900 + Second jeans,Rs.1100

→ Total Cost price = Rs.2000.

• In First Case:

⇒ Gain = Selling price,[S.P] - Cost price,[C.P.]

⇒ Gain = Rs.(990 - 900)

⇒ Gain = Rs.90

• In Second Case:

⇒ Loss = Cost price,[C.P.] - Selling price,[S.P.]

⇒ Loss = Rs.(1100 - 990)

⇒ Loss = Rs.110

Here, condition get loss, So;

→ Total loss = Total S.P. - Total C.P.

→ Total loss = Rs.(110 - 90)

→ Total loss = Rs.20

Now,

We know that Formula of the loss percent, we get;

→ $\bf{Loss\%=\frac{loss}{C.P.} *100}$

→ $\bf{Loss\%=\frac{20}{20\cancel{00}} *\cancel{100}}$

→ $\bf{Loss\%=\cancel{\frac{20}{20} }}$

→ $\bf{\huge{\boxed{Loss\%=1\%}}}$

Thus,

The Loss percent in the whole transaction is 1%.