Question

Mahesh purchased a machine for Rs. 90,000 and sold it at a loss of 20%.
Find the S.P. of the machine.​

Answer 1

GiveN:-

Mahesh purchased a machine for Rs. 90,000 and sold it at a loss of 20%.

To FinD:-

The S.P. of the machine.

SolutioN:-

We know,

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

where,

• SP = ?
• CP = Rs.90,000
• Loss% = 20%

Putting the values,

$\large\implies{\sf{SP=\left(1-\dfrac{20\%}{100}\right)\times90000}}$

$\large\implies{\sf{SP=\left(1-\dfrac{2\cancel{0}}{10\cancel{0}}\right)\times90000}}$

$\large\implies{\sf{SP=\left(1-\dfrac{\cancel{2}}{\cancel{10}}\right)\times90000}}$

$\large\implies{\sf{SP=\left(1-\dfrac{1}{5}\right)\times90000}}$

$\large\implies{\sf{SP=\left(\dfrac{5-1}{5}\right)\times90000}}$

$\large\implies{\sf{SP=\left(\dfrac{4}{5}\right)\times90000}}$

$\large\implies{\sf{SP=\dfrac{4}{\cancel{5}}\times\cancel{90000}}}$

$\large\implies{\sf{SP=4\times18000}}$

$\large\therefore\boxed{\bf{SP=Rs.72,000.}}$

VerificatioN:-

We know that,

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

where,

• SP = Rs.72,000
• CP = Rs.90,000

Putting the values,

$\large\implies{\sf{Loss=Rs.(90,000-72,000)}}$

$\large\therefore\boxed{\bf{Loss=Rs.18,000.}}$

Now,

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

where,

• Loss = Rs.18,000
• Loss% = 20%
• CP = Rs.90,000

Putting the values,

$\large\implies{\sf{20\%=\dfrac{180\cancel{00}}{9\cancel{00}\cancel{00}}\times1\cancel{00}}}$

$\large\implies{\sf{20\%=\dfrac{\cancel{180}}{\cancel{9}}}}$

$\large\implies{\sf{20\%=20\%}}$

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

• Hence verified.

The SP of the machine us Rs.72,000.