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# Aptitude - Alligation or Mixture - Discussion

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"Hold a true friend with both hands."
- (Proverb)
5.

In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?

 [A]. 3 : 7 [B]. 5 : 7 [C]. 7 : 3 [D]. 7 : 5

Explanation:

By the rule of alligation:

 Cost of 1 kg pulses of 1st kind Cost of 1 kg pulses of 2nd kind Rs. 15 Mean Price Rs. 16.50 Rs. 20 3.50 1.50

Required rate = 3.50 : 1.50 = 7 : 3.

 Ladli said: (Wed, Jun 8, 2011 07:23:35 AM) How you got 3.50 and 1.50? Please tell me.

 Manasa said: (Fri, Jun 10, 2011 08:12:29 AM) @ladli (20-16.50):(16.50-15)=3.50:1.50=7:3

 Sheetal said: (Fri, Aug 19, 2011 08:22:45 PM) If cost of 1kg pulses of 2'nd kind is=15 & 1'st kind is=20... then what will be the ans? Please tell me... It's depends upon the mean price?

 Viswajit said: (Sat, Sep 10, 2011 07:23:53 PM) Thank you manasa.

 San said: (Mon, Sep 19, 2011 06:16:16 AM) If we swap 15 and 20 places. Why can't it be 3:7 ? is there any rule?

 Sathish said: (Wed, Jan 4, 2012 06:48:57 PM) How we get 3.50:1.50=7:3?

 Shashank said: (Wed, Jan 18, 2012 03:55:46 AM) 350/100:150/100=35:15=7:3

 Prakash said: (Fri, Feb 10, 2012 12:56:35 PM) Its better to follow simple method boss. Lets assume that price of A be 150 and B is 200. Mixture to sell at 165. Cheaper grocery profit = 165-150 = 15. Dearer grocery loss = 200-165=35. Ratios to sell at 165 is. 35 ---- = 7:3 15

 Atul Verma said: (Thu, May 17, 2012 11:34:59 PM) Let x kg of 1st is taken and (1-x) of 2nd is taken. Then price of mixture will be:15*x+20*(1-x)=20-5x ----(1) Given price of mixture is 16.5 -----(2) From Equation (1) & (2) 20-5x=16.5 => 5x=20-16.5 => x=3.5/5 => x=0.7 So,ratio is x:1-x i.e. 0.7:0.3 => 7:3 ans

 Krishna Teja said: (Tue, Aug 28, 2012 12:53:45 AM) Atul thank you :).

 Vinod said: (Fri, Dec 28, 2012 08:37:05 AM) Let x=15,y=20. We know that x+y=16.50. We can write in eqtion form: 15x+20y = 16.50(x+y) 16.50x-15x = 20y-16.50y 1.50x =3.50y x/y = 3.50/1.50 Just we can convert From eq x = 350/100=35 Eqtion y = 150/100=15 There fore ratio is x:y =35:15. Then answer is 7:3.

 Anup said: (Mon, Dec 31, 2012 09:02:44 PM) @Atul. Really superb solution. Unlike the theoretical approach this is quite simple to understand.

 Kousik Maji said: (Sat, Feb 9, 2013 08:16:19 PM) Let x kg first variety mixed with y kg of second variety. So total cost of(x+y) kg is Rs. 15x+20y. So cost of 1 kg mixture is Rs. (15x+20y)/x+y. Now according to question, (15x+20y)/(x+y)=16.50 => (15x+20y)/(x+y)=33/2 =>33x+33y=30x+40y =>3x=7y => x:y=7:3. Answer is 7:3.