Question

a man sold a toster at a profit of 10% had he purchased it for 5% less than its sold for rupees 56 more he would have gained 25% for how much did he pay​

Answer 1

$\sf\large\underline{Let:}$

• $\rm{Cost\: price\:_{(roster)}=x}$

$\sf\large\underline{To\: Find:}$

• $\rm{Cost\: price\:_{(roster)}=?}$

$\sf\large\underline{Solution:}$

$\sf\small\underline{Given,\:in\:case\:(i):}$

$\rm{A\:man\:sold\:a\:toster\:at\:a\:profit\:of\:10\%}$

$\tt{SP=\dfrac{100+G\%}{100}\times\:CP}$

$\tt{SP=\dfrac{100+10}{100}\times\:x}$

$\tt{SP=\dfrac{110x}{100}}$

$\tt{SP=\dfrac{11x}{10}------(i)}$

$\sf\small\underline{Given,\:in\:case\:(ii):}$

• had he purchased it for 5% less than its sold for rupees 56 more]

$\tt{\implies SP=\dfrac{100-L\%}{100}\times\:CP}$

$\tt{\implies SP=\dfrac{100-5}{100}\times\:x}$

$\tt{\implies SP=\dfrac{95x}{100}+56------(ii)}$

• solving equations 1 and 2 here]

$\tt{\implies \dfrac{11x}{10}=\dfrac{95x}{100}+56}$

$\tt{\implies \dfrac{11x}{10}-\dfrac{95x}{100}=56}$

$\tt{\implies \dfrac{110x-95x}{100}=56}$

$\tt{\implies 15x=5600}$

$\tt{\implies x=373.33}$

$\sf\small\underline{Given,\:in\:case\:(iii):}$

• he would have gained 25% for how much did he pay]

$\tt{\implies CP\:_{(for\: him)}=\frac{100-25}{00}\times\:373.33}$

$\tt{\implies CP\:_{(for\: him)}=\frac{75}{100}\times\:373.33}$

$\tt{\implies CP\:_{(for\: him)}=279.99}$

Answer 2

✓ Given ✓

• Selling Price = 10% profit

• Cost price = 5% less than Selling Price

✓ To find : ✓

If he would have sold it for Rs. 56/- more ;

he would have got 25% profit on the Cost price. ( cost price is the amount he payed or amount for which he had bought the toaster.)

✓ Solution : ✓

Let us consider the cost price of the toaster as : X

We have been told that he had got a profit of 10% when he sold that.

It means SELLING PRICE : $\rm{ x + (\dfrac{10}{100})x}$

So we get the selling price as :

1.1x

COST PRICE : 5% less . so ,

$\rm{ x - \dfrac{5}{100}x }$

So , we get the Cost price as :

0.95x

If he had sold for Rs. 56/- more ; he would have got a profit of 25%

So , 1.1x + 56 = profit of 25%

SELLING PRICE :

$\rm{ 0.95x + (\dfrac{25}{100})0.95x }$

$\implies{\rm{ 1.25 \times 0.95x}}$

When we bring the first and second selling prices together we get the equation :

$\longrightarrow{\rm{ 1.25 \times 0.95x = 1.1x \times 56}}$

$\longrightarrow{\rm{ 0.0875x = 56}}$

Here we have taken approximate value i.e. the nearest value of multiplication as the amount cannot be negative.

$\longrightarrow{\rm{ x = 640}}$

$\large{\implies\boxed{\rm{ CP = Rs. 640/-}}}$