Question

A man sells an article at a profit of 25 %. If he had bought it at 20 % less and sold it for rs 36.75 less he would have gained 30% .find the cost price of the article?

Answer 1

Answer:-

Let the CP of the article be Rs. x.

Given:

A man sells the article at a profit of 25%.

We know that,

SP = CP × (100 + Profit % / 100)

So,

★ SP of the article = x × (100 + 25 / 100)

⟹ SP of the article = 125x / 100

Also given that,

If he had bought it at 20% less and sold it for Rs. 36.75 less he would have gained 30%

So,

In this case;

• CP is decreased by 20%

• SP is also decreased by Rs. 36.75

• Profit % = 30%

Hence,

★ New CP of the article = x × (100 - 20) / 100

⟹ New CP of the article = Rs. 80x/100

★ New SP of the article = (125x/100) - 36.75

⟹ New SP of the article = 125x/100 - 3675/100

⟹ New SP of the article = (125x - 3675) / 100

We know that,

$\boxed{ \sf \: profit \: \% = \frac{sp - cp}{cp} \times 100}$

So,

$\implies \sf \: 30 = \dfrac{ \frac{125x - 3675}{100} - \frac{80x}{100} }{ \frac{80x}{100} } \times 100 \\ \\ \\ \implies \sf \: 30 \times \frac{1}{100} = \frac{125x - 3675 - 80x}{100} \times \frac{100}{80x} \\ \\ \\ \implies \sf \: \frac{30}{100} = \frac{45x - 3675}{80x} \\ \\ \\ \implies \sf \: 30 \times 80x = 100(45x - 3675) \\ \\ \\ \implies \sf \: 2400x = 4500x - 367500 \\ \\ \\ \implies \sf \: 367500 = 4500x - 2400x \\ \\ \\ \implies \sf \: 367500 = 2100x \\ \\ \\ \implies \sf \: \frac{367500}{2100} = x \\ \\ \\ \implies \boxed{\sf \: x = Rs. \: 175}$

∴ The original CP of the article is Rs. 175