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A dealer sold a scooter at a loss of 5.5%. Had he sold it for Rs 1000 more, he would have gained a profit of 4.5%. Find the selling price to gain a profit of 12%.
- ARs. 13,550
- BRs. 12,450
- CRs. 11,200
- DRs. 12,000
Answer not set
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CCommunity
Let cost price of the article be Rs. ‘x’, then,
Selling price in first case = x – x × (5.5/100)
When scooter is sold at Rs. 1000 more, then,
Selling price in second case = x – x × (5.5/100) + 1000 {which gives a profit of 4.5%}
Hence,
$(x - \frac{{5.5}}{{100}}x\; + \;1000\; = \;x\; + \;\frac{{4.5}}{{100}}x)$
⇒ 1000 = (10/100)x
⇒ x = Rs. 10,000 = Cost price of the article.
Now, to gain a profit of 12%,
Selling price of the article = Rs. {10000 × 112/100} = Rs. 11,200
Hence, the required selling price of the article is Rs. 11,200.
Alternate Method (Short trick):
(5.5% + 4.5%) of CP = 1000
⇒ 10% of CP = 1000
⇒ CP = Rs. 10,000
Required selling price to gain 12% = Rs (10000 × 112/100) = Rs. 11,200.
Selling price in first case = x – x × (5.5/100)
When scooter is sold at Rs. 1000 more, then,
Selling price in second case = x – x × (5.5/100) + 1000 {which gives a profit of 4.5%}
Hence,
$(x - \frac{{5.5}}{{100}}x\; + \;1000\; = \;x\; + \;\frac{{4.5}}{{100}}x)$
⇒ 1000 = (10/100)x
⇒ x = Rs. 10,000 = Cost price of the article.
Now, to gain a profit of 12%,
Selling price of the article = Rs. {10000 × 112/100} = Rs. 11,200
Hence, the required selling price of the article is Rs. 11,200.
Alternate Method (Short trick):
(5.5% + 4.5%) of CP = 1000
⇒ 10% of CP = 1000
⇒ CP = Rs. 10,000
Required selling price to gain 12% = Rs (10000 × 112/100) = Rs. 11,200.