Question

an item was sold for Rs . 570 at a loss of 5% . find its cost price .​

Answer 1

GiveN:-

An item was sold for Rs . 570 at a loss of 5% .

To FinD:-

Find its cost price .

SolutioN:-

We know that,

$\large{\green{\underline{\boxed{\bf{SP=\left(1-\dfrac{Loss\%}{100}\right)\times\:CP}}}}}$

where,

• SP = Rs.570
• Loss% = 5%
• CP = ?

Putting the values,

$\large\implies{\sf{570=\left(1-\dfrac{5\%}{100}\right)\times\:CP}}$

$\large\implies{\sf{570=\left(1-\dfrac{\cancel{5}}{\cancel{100}}\right)\times\:CP}}$

$\large\implies{\sf{570=\left(1-\dfrac{1}{20}\right)\times\:CP}}$

$\large\implies{\sf{570=\left(\dfrac{20-1}{20}\right)\times\:CP}}$

$\large\implies{\sf{570=\left(\dfrac{19}{20}\right)\times\:CP}}$

$\large\implies{\sf{570=\dfrac{19}{20}\times\:CP}}$

$\large\implies{\sf{\dfrac{570\times20}{19}=CP}}$

$\large\implies{\sf{\dfrac{\cancel{570}\times20}{\cancel{19}}=CP}}$

$\large\implies{\sf{30\times20=CP}}$

$\large\implies{\sf{600=CP}}$

$\large\therefore\boxed{\bf{CP=Rs.600.}}$

VerificatioN:-

We know that,

$\large{\green{\underline{\boxed{\bf{Loss=CP-SP}}}}}$

where,

• CP = Rs.600
• SP = Rs.570

Putting the values,

$\large\implies{\sf{Loss=Rs.(600-570)}}$

$\large\therefore\boxed{\bf{Loss=Rs.30}}$

Now,

$\large{\green{\underline{\boxed{\bf{Loss\%=\dfrac{Loss}{CP}\times100}}}}}$

where,

• Loss% = 5%
• CP = Rs.600
• Loss = Rs.30

Putting the values,

$\large\implies{\sf{5\%=\dfrac{30}{600}\times100}}$

$\large\implies{\sf{5\%=\dfrac{30}{6\cancel{00}}\times1\cancel{00}}}$

$\large\implies{\sf{5\%=\dfrac{30}{6}}}$

$\large\implies{\sf{5\%=\dfrac{\cancel{30}}{\cancel{6}}}}$

$\large\implies{\sf{5\%=5\%}}$

$\large\therefore\boxed{\bf{LHS=RHS.}}$

• Hence verified.

The Cost Price is Rs.600.