Question

A shopekeeper sells one machine for 990 rupees at profit 10% and another machine for 1960 rupees at loss of 2% what is his gain or loss percentage​

Answer 1

Answer:-

Given:

SP of a machine = Rs. 990

Profit% = 10 %

SP of other machine = Rs. 1960

loss% = 2 %

We know that,

CP * (100 + profit%)/100 = SP

So,

First machine :

CP * (100 + 10)/100 = 990

⟹ CP = 990 * 100/110

⟹ CP = Rs. 900

Second machine :

We know that,

CP * (100 - loss%)/100 = SP

⟹ CP * (100 - 2)/100 = 1960

⟹ CP = 1960 * 100/98

⟹ CP = Rs. 2000

Now,

We have to find the total loss or profit percentage.

• Total SP = 990 + 1960 = Rs. 2950
• Total CP = 900 + 2000 = Rs. 2900.

We observe that,

SP > CP.

so, a gain is occured.

gain % = gain/CP * 100

gain = SP - CP

So,

gain% = (2950 - 2900)/2900 * 100

⟹ gain% = 50/29

⟹ gain% = 1.72 %

∴ A gain of 1.72% is occured in the whole transaction.

Answer 2

$\huge\bf{\underline{\underline{\gray{GIVEN:-}}}}$

• A shopkeeper sells,

1. One machine for Rs.990 at profit of 10% .
2. Another machine for Rs.1960 at loss of 2% .

$\huge\bf{\underline{\underline{\gray{TO\:FIND:-}}}}$

• His gain or loss percentage .

$\huge\bf{\underline{\underline{\gray{SOLUTION:-}}}}$

ᴄᴀsᴇ - 1 ;-

☯︎ In the first transaction,

${\color{aqua}\bigstar}\:\bf{\pink{\overbrace{\underbrace{\blue{C.P\:=\:\dfrac{S.P\times{100}}{100\:+\:\%{Profit}}\:}}}}}$

$\\ \bf{:\implies\:C.P\:=\:\dfrac{990\times{100}}{100\:+\:10}\:}$

$\\ \bf{:\implies\:C.P\:=\:\dfrac{99000}{110}\:}$

$\\ \bf\green{:\implies\:C.P\:=\:Rs.900\:}$

ᴄᴀsᴇ - 2 ;-

☯︎ In the second transaction,

$\purple\bigstar\:\bf{\red{\overbrace{\underbrace{\green{C.P\:=\:\dfrac{S.P\times{100}}{100\:-\:\%{Loss}}\:}}}}}$

$\\ \bf{:\implies\:C.P\:=\:\dfrac{1960\times{100}}{100\:-\:2}\:}$

$\\ \bf{:\implies\:C.P\:=\:\dfrac{196000}{98}\:}$

$\\ \bf\green{:\implies\:C.P\:=\:Rs.2000\:}$

So,

$\bf{:\implies\:Total\:C.P\:=\:Rs.\:(900\:+\:2000)\:}$

$\\ \bf\gray{:\implies\:Total\:C.P\:=\:Rs.2900\:}$

And

$\bf{:\implies\:Total\:S.P\:=\:Rs.\:(990\:+\:1960)\:}$

$\\ \bf\gray{:\implies\:Total\:S.P\:=\:Rs.2950\:}$

Since,

• S.P > C.P

✈︎ Hence here gain or profit is occured .

✯ Pʀᴏғɪᴛ = S.ᴘ - C.ᴘ

➤ Pʀᴏғɪᴛ = 2950 - 2900

➤ Pʀᴏғɪᴛ = Rs.50

$\huge\red\checkmark$ $\bf\orange{Gain\%\:=\:\dfrac{Profit}{C.P}\times{100}\:}$

$\\ \bf{:\implies\:Gain\%\:=\:\dfrac{50}{2900}\times{100}\:}$

$\\ \bf{:\implies\:Gain\%\:=\:\dfrac{5000}{2900}\:}$

$\\ \bf\blue{:\implies\:Gain\%\:=\:1.724\%\:}$

$\huge{\color{orange}\therefore}$ The gain% is '1.724%' .