Some amount of sugar costing Rs. 9 per kg is mixed with 27 kg of sugar costing Rs. 7 per kg. There is a gain of 10% by selling the mixture at Rs. 9.24 per kg. In what ratio both the qualities of sugar have been mixed?
Some amount of sugar costing Rs. 9 per kg is mixed with 27 kg of sugar costing Rs. 7 per kg. There is a gain of 10% by selling the mixture at Rs. 9.24 per kg. In what ratio both the qualities of sugar have been mixed?
1). 3 ∶ 4
2). 3 ∶ 5
3). 7 ∶ 3
4). 2 ∶ 5
1 answers
Selling price of 1 kg of the mixture = Rs. 9.24
Gain % = 10%
Let the cost price of 1 kg of the mixture = Rs. x
By the formula of Cost price, CP + 10% of CP = SP
$(\begin{array}{l} \Rightarrow x + \frac{{10}}{{100}} \times x = 9.24\\ \Rightarrow \frac{{110}}{{100}} \times x = 9.24 \end{array})$
∴ x = Rs. 8.40
Cost of 1 kg sugar of 1st quality = Cost price of dearer = d = Rs. 9
Cost of 1 kg sugar of 2nd quality = Cost price of cheaper = c = Rs. 7
Cost of 1 kg of the mixture = Mean price = m = Rs.8.40
By formula,
$(\begin{array}{l} \frac{{{\rm{Quantity\;of\;Cheaper}}}}{{{\rm{Quantity\;of\;Dearer}}}} = \frac{{{\rm{d}} - {\rm{m}}}}{{{\rm{m}} - {\rm{c}}}}\\ \Rightarrow \frac{{9 - 8.40}}{{8.40 - 7}} = \frac{3}{7} \end{array})$
∴ The ratio of dearer to cheaper or 1st quality : 2nd quality is 7 : 3Other Questions
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