RPF Constable practice question
A man sold an article at a loss of $10\%$. Had he sold it for ₹90 more, he would have gained $8\%$. Find the cost price.
From a RPF Constable Quantitative Aptitude practice set · Quantitative Aptitude
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Correct answer: (A) ₹500
### **Given:**
- Initial condition: Loss = $10\%$
- If Selling Price is increased by ₹90, Profit = $8\%$
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### **Method 1: Percentage Difference Method**
1. Let the Cost Price ($\text{CP}$) be $100\%$.
2. Initial Selling Price ($\text{SP}_1$) at $10\%$ loss:
$$\text{SP}_1 = 100\% - 10\% = 90\% \text{ of } \text{CP}$$
3. New Selling Price ($\text{SP}_2$) at $8\%$ profit:
$$\text{SP}_2 = 100\% + 8\% = 108\% \text{ of } \text{CP}$$
4. The difference between the two selling prices corresponds to ₹90:
$$\text{Difference} = \text{SP}_2 - \text{SP}_1 = 108\% - 90\% = 18\% \text{ of } \text{CP}$$
5. Equating the difference:
$$18\% \text{ of } \text{CP} = ₹90$$
$$\text{CP} = \frac{90}{18} \times 100 = 5 \times 100 = ₹500$$
---
### **Method 2: Algebraic Method**
Let the Cost Price be $x$.
$$\text{SP}_1 = 0.90x$$
$$\text{SP}_2 = 1.08x$$
Given:
$$\text{SP}_2 - \text{SP}_1 = 90$$
$$1.08x - 0.90x = 90$$
$$0.18x = 90$$
$$x = \frac{90}{0.18} = ₹500$$
---
### **Conclusion:**
The cost price of the article is **₹500**.
- Initial condition: Loss = $10\%$
- If Selling Price is increased by ₹90, Profit = $8\%$
---
### **Method 1: Percentage Difference Method**
1. Let the Cost Price ($\text{CP}$) be $100\%$.
2. Initial Selling Price ($\text{SP}_1$) at $10\%$ loss:
$$\text{SP}_1 = 100\% - 10\% = 90\% \text{ of } \text{CP}$$
3. New Selling Price ($\text{SP}_2$) at $8\%$ profit:
$$\text{SP}_2 = 100\% + 8\% = 108\% \text{ of } \text{CP}$$
4. The difference between the two selling prices corresponds to ₹90:
$$\text{Difference} = \text{SP}_2 - \text{SP}_1 = 108\% - 90\% = 18\% \text{ of } \text{CP}$$
5. Equating the difference:
$$18\% \text{ of } \text{CP} = ₹90$$
$$\text{CP} = \frac{90}{18} \times 100 = 5 \times 100 = ₹500$$
---
### **Method 2: Algebraic Method**
Let the Cost Price be $x$.
$$\text{SP}_1 = 0.90x$$
$$\text{SP}_2 = 1.08x$$
Given:
$$\text{SP}_2 - \text{SP}_1 = 90$$
$$1.08x - 0.90x = 90$$
$$0.18x = 90$$
$$x = \frac{90}{0.18} = ₹500$$
---
### **Conclusion:**
The cost price of the article is **₹500**.
हिंदी में प्रश्न
एक व्यक्ति ने एक वस्तु $10\%$ हानि पर बेची। यदि वह इसे ₹90 अधिक में बेचता, तो उसे $8\%$ लाभ होता। वस्तु का क्रय मूल्य ज्ञात कीजिए।
उत्तर जाँचने के लिए किसी विकल्प पर टैप करें।
उत्तर और व्याख्या देखें
सही उत्तर: (A) ₹500
### **दिया गया है:**
- प्रारंभिक स्थिति: हानि = $10\%$
- यदि विक्रय मूल्य ₹90 अधिक होता, तो लाभ = $8\%$
---
### **विधि 1: प्रतिशत अंतर विधि**
1. माना कि क्रय मूल्य ($\text{CP}$) $100\%$ है।
2. $10\%$ हानि पर पहला विक्रय मूल्य ($\text{SP}_1$):
$$\text{SP}_1 = 100\% - 10\% = 90\%$$
3. $8\%$ लाभ पर नया विक्रय मूल्य ($\text{SP}_2$):
$$\text{SP}_2 = 100\% + 8\% = 108\%$$
4. दोनों विक्रय मूल्यों के बीच का प्रतिशत अंतर:
$$\text{अंतर} = 108\% - 90\% = 18\%$$
5. यह $18\%$ अंतर ₹90 के बराबर है:
$$18\% \text{ of } \text{CP} = ₹90$$
$$\text{CP} = \frac{90}{18} \times 100 = 5 \times 100 = ₹500$$
---
### **विधि 2: बीजगणितीय विधि**
माना क्रय मूल्य $x$ है।
$$\text{SP}_1 = 0.90x$$
$$\text{SP}_2 = 1.08x$$
प्रश्नानुसार:
$$\text{SP}_2 - \text{SP}_1 = 90$$
$$1.08x - 0.90x = 90$$
$$0.18x = 90$$
$$x = \frac{90}{0.18} = ₹500$$
---
### **निष्कर्ष:**
अतः वस्तु का क्रय मूल्य **₹500** है।
- प्रारंभिक स्थिति: हानि = $10\%$
- यदि विक्रय मूल्य ₹90 अधिक होता, तो लाभ = $8\%$
---
### **विधि 1: प्रतिशत अंतर विधि**
1. माना कि क्रय मूल्य ($\text{CP}$) $100\%$ है।
2. $10\%$ हानि पर पहला विक्रय मूल्य ($\text{SP}_1$):
$$\text{SP}_1 = 100\% - 10\% = 90\%$$
3. $8\%$ लाभ पर नया विक्रय मूल्य ($\text{SP}_2$):
$$\text{SP}_2 = 100\% + 8\% = 108\%$$
4. दोनों विक्रय मूल्यों के बीच का प्रतिशत अंतर:
$$\text{अंतर} = 108\% - 90\% = 18\%$$
5. यह $18\%$ अंतर ₹90 के बराबर है:
$$18\% \text{ of } \text{CP} = ₹90$$
$$\text{CP} = \frac{90}{18} \times 100 = 5 \times 100 = ₹500$$
---
### **विधि 2: बीजगणितीय विधि**
माना क्रय मूल्य $x$ है।
$$\text{SP}_1 = 0.90x$$
$$\text{SP}_2 = 1.08x$$
प्रश्नानुसार:
$$\text{SP}_2 - \text{SP}_1 = 90$$
$$1.08x - 0.90x = 90$$
$$0.18x = 90$$
$$x = \frac{90}{0.18} = ₹500$$
---
### **निष्कर्ष:**
अतः वस्तु का क्रय मूल्य **₹500** है।
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