Question

The cost price of a box and a pen is Rs80.The box is sold at 10%profit and the pen is sold at 10% loss. If the selling price of the box is Rs28 more than that of the pen ,calculate the profit or loss percent in the whole.

Answer 1

Answer:-

$\red{\bigstar}$$\large\boxed{\rm\purple{Profit\% - 2.5\%}}$

• Given:-

Cost Price of box and a pen = Rs. 80

Profit% on box = 10%

Loss% on pen = 10%

• To Find:-

Profit or Loss

• Solution:-

Let the C.P of box be "Rs. x".

C.P of pen = Rs. 80 - x

$\pink{\bigstar}$ Box is sold at 10% Profit:-

→ S.P of box = C.P of box + Profit

→ S.P of box = $\sf{x + \dfrac{10}{100}x}$

→ S.P of box = $\bf\red{Rs. \: 1.1 x}$

$\pink{\bigstar}$ Pens are sold at 10% loss:-

→ S.P of pen = C.P of pen - Loss

→ S.P of pen = $\sf{(80 - x) - \dfrac{10}{100}(80-x)}$

→ S.P of pen = $\sf{80 - x - 0.1(80 - x)}$

→ S.P of pen = $\sf{80 - x - 8 - 0.1x}$

→ S.P of pen = $\bf\red{Rs. \: 72 - 0.9 x}$

$\pink{\bigstar}$ S.P of box:-

→ S.P of box = 28 + SP of pen

→ $\sf{1.1x = 28 + 72 - 0.9x}$

→ $\sf{1.1x = 100 - 0.9x}$

→ $\sf{1.1x + 0.9 x = 100}$

→ $\sf{2x = 100}$

→ $\bf\red{x = 50}$

$\pink{\bigstar}$ Total SP:-

Total SP = $\sf{1.1x + 72 - 0.9x}$

→ $\sf{72 + 0.2 x}$

→ $\sf{72 + 0.2 \times 50}$

→ $\sf{72 + 10}$

→ $\bf\red{Rs. \: 82}$

• Total SP = Rs. 82

• Total CP = Rs. 80

here,

S.P > C.P

Hence, Profit

✧ Profit = S.P - C.P

→ $\sf{82 - 80}$

→ $\bf\red{Rs. \: 2}$

✧ Profit% = Profit/C.P × 100

→ $\sf{\dfrac{2}{80} \times 100}$

→ $\sf{\dfrac{200}{80}}$

→ $\sf{\dfrac{5}{2}}$

→ $\large\bf\red{2.5 \%}$

Answer 2

ʟᴇᴛ ꜱᴀʏ ᴄᴏꜱᴛ ᴘʀɪᴄᴇ ᴏꜰ ʙᴏx = ʀꜱ x

ᴛʜᴇɴ ᴄᴏꜱᴛ ᴘʀɪᴄᴇ ᴏꜰ ᴘᴇɴ = ʀꜱ 80 - x

ʙᴏx ɪꜱ ꜱᴏʟᴅ ᴀᴛ 10% ᴘʀᴏꜰɪᴛ ꜱᴏ

ʙᴏx ꜱᴇʟʟɪɴɢ ᴘʀɪᴄᴇ = .ʙᴏx ᴄᴏꜱᴛ ᴘʀɪᴄᴇ + ᴘʀᴏꜰɪᴛ  

=> Bᴏx ꜱᴇʟʟɪɴɢ ᴘʀɪᴄᴇ = .x + (10/100).x = ʀꜱ 1.1.x

ᴘᴇɴ ɪꜱ ꜱᴏʟᴅ ᴀᴛ 10 % ʟᴏꜱꜱ

ᴘᴇɴ ꜱᴇʟʟɪɴɢ ᴘʀɪᴄᴇ = (80-.x) - (10/100)(80-.x)  = ʀꜱ 72 - 0.9.x

ꜱᴘ ᴏꜰ ʙᴏx = 28 + ꜱᴘ ᴏꜰ ᴘᴇɴ

=> 1.1x = 28 + 72 - 0.9.x  

=> 2x = 100

=> x = 50

ᴛᴏᴛᴀʟ ꜱᴇʟʟɪɴɢ ᴘʀɪᴄᴇ = 1.1.x + 72 - 0.9.x = 72 + 0.2.x

= 72 + 0.2*50

= 72 + 10

= 82

ᴛᴏᴛᴀʟ ꜱᴘ = ʀꜱ 82

ᴛᴏᴛᴀʟ ᴄᴘ = ʀꜱ 80

ᴘʀᴏꜰɪᴛ = 82 - 80 = ʀꜱ 2

ᴘʀᴏꜰɪᴛ % = (2/80)*100 = 2.5%