Question

एक थोक विक्रेता ने एक मशीन 20% लाभ पर एक दुकानदार को बेची। दुकानदार ने इसे ग्राहक को 25% लाभ पर बेच दिया।
दकानदार और थोक विक्रेता के विक्रय-मूल्यों में ₹ 129 का अन्तर पाया गया। मशीन का प्रारम्भिक मूल्य ज्ञात करो।
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Answer 1

Given:

एक थोक विक्रेता ने एक मशीन 20% लाभ पर एक दुकानदार को बेची।

दुकानदार ने इसे ग्राहक को 25% लाभ पर बेच दिया।

दकानदार और थोक विक्रेता के विक्रय-मूल्यों में ₹ 129 का अन्तर पाया गया।

To find:

मशीन का प्रारम्भिक मूल्य ज्ञात करो।

Solution:

Let's assume "x" represents the initial cost price of the machine.

For Wholesaler:

The S.P. of the machine = $\frac{100 + G\%}{100} \times C.P. = \frac{100 + 20}{100} \times x = \frac{6}{5} x$

S.P. of wholesaler = C.P. of the shopkeeper = $\frac{6x}{5}$

For Shopkeeper:

The S.P. of the machine = $\frac{100 + G\%}{100} \times C.P. = \frac{100 + 25 }{100} \times \frac{6x}{5} = \frac{125 }{100} \times \frac{6x}{5} = \frac{3x}{2}$

Now,

The difference between the selling prices of the shopkeeper and the wholesaler = 129

i.e., [S.P. of shopkeeper] - [S.P. of wholesaler] = 129

⇒ $\frac{3x}{2} - \frac{6x}{5} = 129$

⇒ $\frac{15x - 12x}{10} = 129$

⇒ $\frac{3x}{10} = 129$

⇒ $3x = 1290$

⇒ $x = \frac{1290}{3}$

⇒ $\bold{x = 430}$

Thus, the initial price of the machine was → Rs. 430.

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