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Given: Water has to be mixed in milk such that a profit of 12% is obtained upon selling the mixture at cost price. Formula: (Cheaper quantity) : (Dearer quantity) = (d - m) : (m - c) Calculation: Let cost price of milk be Re 1 Then, selling price of mixture will also be Rs. 1 Gain = 12% Cost price of mixture = 1 × (100/112) = 25/28 Ratio to be mixed = [1 – (25/28)] : [(25/28) – 0] ⇒ (3/28) : (25/28) ⇒ 3 : 25 ∴ The proportion to be mixed is 3 : 25 India’s #1 Learning Platform Start Complete Exam Preparation
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Answer: Option C Explanation: Let CP of 1 litre milk = Rs.1SP of 1 litre mixture = CP of 1 litre milk = Rs.1Gain $=16\dfrac{2}{3}\%=\dfrac{50}{3}\%$CP of 1 litre mixture $=\dfrac{100}{\left(100 + \text{Gain}\% \right)}× \text{SP}$ $=\dfrac{100}{\left(100+\dfrac{50}{3}\right)}× 1=\dfrac{100}{\left(\dfrac{350}{3}\right)}\\=\dfrac{300}{350}=\dfrac{6}{7}$
Quantity of water : Quantity of milk $=\dfrac{1}{7}:\dfrac{6}{7}=1:6$
Let c.p. of milk = re 1, then s.p. of Mixture = c.p. of milk = re 1 given gain= 50/3% gain amount = 50/3% of 1 = 50/300 = 1/6 We know that, C.P. of Mixture = S.p. of mixture - gain on mixture = 1 - 1/6 = 5/6 Now require ratio = d-m : m-c 1-5/6 : 5/6 - 0 1/6 : 5/6 1:5. so, I think Your answer is wrong. Let c.p. of milk = re 1, then<p>s.p. of Mixture = c.p. of milk = re 1</p><p>given gain= 50/3%</p><p>gain amount = 50/3% of 1 = 50/300 = 1/6</p><p>We know that,</p><p>C.P. of Mixture = S.p. of mixture - gain on mixture</p><p> = 1 - 1/6 = 5/6</p><p>Now require ratio = d-m : m-c</p><p> 1-5/6 : 5/6 - 0</p><p> 1/6 : 5/6</p><p> 1:5.</p><p>so, I think Your answer is wrong. </p>still i am not understanding what u did ajay Dear Ajay,The answer given is right. Let me explain where u went wrong. C.P. of Mixture is not 5/6You calculated the gain amount as 50/3% of 1 = 50/300 = 1/6 which is wrongThe gain has to be calculated on the CP of the mixture as we are selling the mixture.Hence you can not consider it as 50/3% of 1 as the 1 is the CP of 1 litre milk, not the CP of 1 litre mixture) Hence, to get the answer, you need to find out the CP of the mixture from the SP of the mixture and the gain% Dear Ajay,The answer given is right. Let me explain where u went wrong. C.P. of Mixture is not 5/6You calculated the gain amount as 50/3% of 1 = 50/300 = 1/6 which is wrongThe gain has to be calculated on the CP of the mixture as we are selling the mixture.Hence you can not consider it as 50/3% of 1 as the 1 is the CP of 1 litre milk, not the CP of 1 litre mixture)<p>Hence, to get the answer, you need to find out the CP of the mixture from the SP of the mixture and the gain%</p>
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