Question

A micro oven was sold at a profit of 9% , if it had been sold at a profit of 12%, the profit would have been Rs 729 more. find its cost price.​

Answer 1

Question :-

A micro oven was sold at a profit of 9% , if it had been sold at a profit of 12%, the profit would have been Rs 729 more. find its cost price.

Answer :-

→ Cost price = Rs. 24300

To Find :-

→ Cost price of oven .

Explanation :-

According to the question -

→ It was sold at profit of 9% and its has been sold at profit of 12% hence -

Let , cost price is "x" , selling price "y",-

According to the condition - it had more 729

$\to \sf \: x \: of \: 12\% = y + 729 \\ \\ \to \sf \frac{12x}{100} = y + 729 \: \: ....eq.(1) \:$

and ,when sold at 9%

$\to \sf \: x \: of \:9\% = y \\ \\ \to \sf \frac{9x}{100} = y \: \: .....eq.(2)$

Put the value of "y" from equation (2) in eq.(1)

$\mapsto \sf \frac{12x}{100} = \frac{9x}{100} + 729 \\ \\ \mapsto \sf \: \frac{12x}{100} - \frac{9x}{100} = 729 \\ \\ \mapsto \sf \: \frac{x(12 - 9)}{100} = 729 \\ \\ \mapsto \sf \: \frac{3x}{100} = 729 \\ \\ \mapsto \sf \: x = \frac{72900}{3} \\ \\ \to \boxed{\sf \: x = 24300}$

Hence ,cost price is Rs. 24300

Answer 2

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➠ To Find :

Cost Price of micro often.

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➠ Solution :

Let cost price of the micro often be a and b.

So,

Case 1 :-

$\sf{a \: of \: 12 \% = y + 729} \\ \\ \sf{\frac{12a}{100} = y + 729 ....</p><p>.(1)}$

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Case 2 :-

$\sf{a \: of \: 9 \% = b} \\ \\ \sf{\frac{9a}{100} = b......(1)}$

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From equation 1 and 2.

$\sf \frac{12x}{100} = \frac{9x}{100} + 729 \\ \\ \implies \sf \: \frac{12x}{100} - \frac{9x}{100} = 729 \\ \\ \bf{Taking \: L. C. M} \\ \\ \implies \sf \: \frac{12x - 9x}{100} = 729 \\ \\ \implies \sf \: \frac{3x}{100} = 729 \\ \\ \implies \sf \: x = \frac{72900}{3} \\ \\ \sf{ \: x = 24300}$

$\sf{\therefore}$ Cost price is Rs. 24,300