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9. How many kilograms of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10 % by selling the mixture at Rs. 9.24 per kg? | |

A. 56 kg | B. 58 kg |

C. 63 kg | D. 60 kg |

Answer: Option C

Explanation:

Selling Price(SP) of 1 kg mixture= Rs. 9.24

Profit = 10%

Cost Price(CP) of 1 kg mixture $=\dfrac{100}{(100+\text{Profit}\%)}× \text{SP}$

$=\dfrac{100}{(100+10)}× 9.24\\= \dfrac{100}{110}× 9.24=\dfrac{92.4}{11}=\text{ Rs.} 8.4$

By rule of alligation,

CP of 1 kg sugar of 1st kind | CP of 1 kg sugar of 2nd kind | |||||||||

Rs. 9 | Rs. 7 | |||||||||

Mean Price | ||||||||||

Rs.8.4 | ||||||||||

8.4 - 7 = 1.4 | 9 - 8.4 = 0.6 |

i.e., to get a cost price of 8.4, the sugars of kind1 and kind2 should be mixed in the ratio 1.4 : 0.6 = 14 : 6 = 7 : 3

Suppose $x$ kg of kind1 sugar is mixed with 27 kg of kind2 sugar.

then $x$ : 27 = 7 : 3

$\Rightarrow 3x=27×7\\\Rightarrow x=9×7=63$

Narendra

2013-11-16 19:18:50

Pl explain how you reached this answer

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