Question

Find SP or CP in the following problems: (a) CP = 700 , Profit = 12%
(b) SP = 1350, Loss = 10%​

Answer 1

Step-by-step explanation:

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Answer 2

GiveN:-

• (a) CP = 700 , Profit = 12%
• (b) SP = 1350, Loss = 10%

To FinD:-

Find SP or CP in the following problems.

SolutioN:-

• (a) CP = 700 , Profit = 12%
• Here we have to find the SP.

We know that,

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

where,

• SP = ?
• CP = Rs.700
• Profit = 12%

Putting the values,

$\large\implies{\sf{SP=\left(1+\dfrac{12\%}{100}\right)\times\:700}}$

$\large\implies{\sf{SP=\left(1+\dfrac{\cancel{12}}{\cancel{100}}\right)\times\:700}}$

$\large\implies{\sf{SP=\left(1+\dfrac{3}{25}\right)\times\:700}}$

$\large\implies{\sf{SP=\left(\dfrac{25+3}{25}\right)\times\:700}}$

$\large\implies{\sf{SP=\left(\dfrac{28}{25}\right)\times\:700}}$

$\large\implies{\sf{SP=\dfrac{28}{\cancel{25}}\times\:\cancel{700}}}$

$\large\implies{\sf{SP=28\times\:28}}$

$\large\therefore\boxed{\bf{SP=Rs.784.}}$

VerificatioN:-

We know that,

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

where,

• SP = Rs.784
• CP = Rs.700

Putting the values,

$\large\implies{\sf{Profit=Rs.(784-700)}}$

$\large\therefore\boxed{\bf{Profit=Rs.84.}}$

Now,

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

where,

• Profit = Rs.84
• CP = Rs.700
• Profit% = 12%

Putting the values,

$\large\implies{\sf{12\%=\dfrac{84}{700}\times100}}$

$\large\implies{\sf{12\%=\dfrac{84}{7\cancel{00}}\times1\cancel{00}}}$

$\large\implies{\sf{12\%=\dfrac{\cancel{84}}{\cancel{7}}}}$

$\large\implies{\sf{12\%=12\%}}$

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

• Hence verified.

The Selling Price is Rs.784.

______________________________

• (b) SP = 1350 , Profit = 10%
• Here we have to find the CP.

We know that,

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

where,

• CP = ?
• SP = Rs.1350
• Loss = 10%

Putting the values,

$\large\implies{\sf{1350=\left(1-\dfrac{10\%}{100}\right)\times\:CP}}$

$\large\implies{\sf{1350=\left(1-\dfrac{\cancel{10}}{\cancel{100}}\right)\times\:CP}}$

$\large\implies{\sf{1350=\left(1-\dfrac{1}{10}\right)\times\:CP}}$

$\large\implies{\sf{1350=\left(\dfrac{10-1}{10}\right)\times\:CP}}$

$\large\implies{\sf{1350=\left(\dfrac{9}{10}\right)\times\:CP}}$

$\large\implies{\sf{\dfrac{1350\times10}{9}=CP}}$

$\large\implies{\sf{\dfrac{\cancel{1350}\times10}{\cancel{9}}=CP}}$

$\large\implies{\sf{150\times10=CP}}$

$\large\therefore\boxed{\bf{CP=Rs.1500.}}$

VerificatioN:-

We know that,

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

where,

• CP = Rs.1500
• SP = Rs.1350

Putting the values,

$\large\implies{\sf{Profit=Rs.(1500-1350)}}$

$\large\therefore\boxed{\bf{Profit=Rs.150.}}$

Now,

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

where,

• Loss = Rs.150
• CP = Rs.1500
• Loss% = 10%

Putting the values,

$\large\implies{\sf{10\%=\dfrac{150}{1500}\times100}}$

$\large\implies{\sf{10\%=\dfrac{150}{15\cancel{00}}\times1\cancel{00}}}$

$\large\implies{\sf{10\%=\dfrac{\cancel{150}}{\cancel{15}}}}$

$\large\implies{\sf{10\%=10\%}}$

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

• Hence verified.

The Cost Price is Rs.1500.