IB ACIO Grade II practice question
A shopkeeper bought two ceiling fans together for a total of Rs. 8,200. He sold both fans at the same selling price, making a profit of 15% on the first fan and a loss of 10% on the second fan. Find the selling price of each fan.
From a IB ACIO Grade II Quantitative Aptitude practice set · Quantitative Aptitude
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Correct answer: (B) Rs. 4,140
Step 1: Let CP1 be the cost price of the first fan (15% profit) and CP2 the cost price of the second fan (10% loss), with CP1 + CP2 = 8200.
Both give the same SP, so:
CP1 × 1.15 = CP2 × 0.9
CP2 = CP1 × (1.15/0.9) = CP1 × (23/18)
Step 2: Substitute into the sum: CP1 + CP1×(23/18) = 8200
CP1 × (41/18) = 8200
CP1 = 8200 × 18/41 = Rs. 3,600
Step 3: Then CP2 = 8200 − 3600 = Rs. 4,600.
Step 4: SP = CP1 × 1.15 = 3600 × 1.15 = Rs. 4,140. (Check: CP2 × 0.9 = 4600 × 0.9 = Rs. 4,140 ✓)
So each fan was sold for Rs. 4,140.
Both give the same SP, so:
CP1 × 1.15 = CP2 × 0.9
CP2 = CP1 × (1.15/0.9) = CP1 × (23/18)
Step 2: Substitute into the sum: CP1 + CP1×(23/18) = 8200
CP1 × (41/18) = 8200
CP1 = 8200 × 18/41 = Rs. 3,600
Step 3: Then CP2 = 8200 − 3600 = Rs. 4,600.
Step 4: SP = CP1 × 1.15 = 3600 × 1.15 = Rs. 4,140. (Check: CP2 × 0.9 = 4600 × 0.9 = Rs. 4,140 ✓)
So each fan was sold for Rs. 4,140.
हिंदी में प्रश्न
एक दुकानदार ने दो सीलिंग फैन कुल मिलाकर रु. 8,200 में खरीदे। उसने दोनों फैन एक ही विक्रय मूल्य पर बेचे, जिसमें पहले फैन पर उसे 15% लाभ हुआ और दूसरे फैन पर 10% हानि हुई। प्रत्येक फैन का विक्रय मूल्य ज्ञात कीजिए।
उत्तर जाँचने के लिए किसी विकल्प पर टैप करें।
उत्तर और व्याख्या देखें
सही उत्तर: (B) रु. 4,140
चरण 1: मान लीजिए क्रय मूल्य1 पहले फैन का क्रय मूल्य है (15% लाभ) और क्रय मूल्य2 दूसरे फैन का (10% हानि), जहाँ क्रय मूल्य1 + क्रय मूल्य2 = 8200।
दोनों का विक्रय मूल्य समान है, इसलिए:
क्रय मूल्य1 × 1.15 = क्रय मूल्य2 × 0.9
क्रय मूल्य2 = क्रय मूल्य1 × (1.15/0.9) = क्रय मूल्य1 × (23/18)
चरण 2: योग में रखें: क्रय मूल्य1 + क्रय मूल्य1×(23/18) = 8200
क्रय मूल्य1 × (41/18) = 8200
क्रय मूल्य1 = 8200 × 18/41 = रु. 3,600
चरण 3: तब क्रय मूल्य2 = 8200 − 3600 = रु. 4,600।
चरण 4: विक्रय मूल्य = क्रय मूल्य1 × 1.15 = 3600 × 1.15 = रु. 4,140। (जांच: क्रय मूल्य2 × 0.9 = 4600 × 0.9 = रु. 4,140 ✓)
अतः प्रत्येक फैन रु. 4,140 में बेचा गया।
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