What ratio must a grocer mix two varieties of sugar worth Rs 60 a kg and Rs 65 a kg so that by selling the mixture at Rs 68.20 a kg he may gain 10 %?

Discussion :: Alligation or Mixture - General Questions (Q.No.12)

12.

In what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg and Rs. 65 a kg so that by selling the mixture at Rs. 68.20 a kg he may gain 10%?

[A].	3 : 2
[B].	3 : 4
[C].	3 : 5
[D].	4 : 5

Answer: Option A

Explanation:

S.P. of 1 kg of the mixture = Rs. 68.20, Gain = 10%.

C.P. of 1 kg of the mixture = Rs.		100	x 68.20		= Rs. 62.
110

By the rule of alligation, we have:

Cost of 1 kg tea of 1st kind. Cost of 1 kg tea of 2nd kind.
Rs. 60	Mean Price Rs. 62	Rs. 65
3	2

Required ratio = 3 : 2.

Sumeet said: (Jul 27, 2011)
How the required ratio is obtained?

Arpit Jain said: (Sep 1, 2012)
Ratio is obtained by difference between them... 62-60 = 2 65-62 = 3

Simit said: (Aug 3, 2013)
Let us assume x/y ratio. Now x+y = 1. x/y+1 = 1/y ---- (1). Now price, 60x+65y = 62. 60(x/y)+65 = 62[(x/y)+1]. Now this shows that difference become ratio.

Pandia said: (Sep 8, 2013)
603+652 = 180+130. 310 this total 5 kg rate 3 60 kg and 2 65kg. So one kg 310/5 = 62 this is cost price so the ratio of mixture is 3:2.

Swejal said: (May 17, 2014)
Can someone please explain the 2nd step i.e C.P of 1 kg.

Rishabh said: (May 23, 2014)
As we know %gain means %gain over CP =SP - CP. Hence,10% * CP =SP - CP. Upon solving you will get CP=100/110 * SP.

Usha said: (Aug 20, 2015)
Can any one explain how 110/100*68.20 = Rs. 62?

Muna said: (Aug 20, 2015)
How to find out mean price?

Sumanth Geras said: (Aug 20, 2015)
Easy method applicable for all these kinds of problems. (quantity 1price 1+quantity 2price 2)/quantity 1+quantity 2 = mean quantity. Since it is given that he got 10 % profit so this 10% is for additional money which is added to mean value obtained (i.e 10% of 68.20 is 62 approximately). (60(x)+65(y))/x+y = 62. If you solve it you get 3:2.

Krishna said: (Sep 22, 2015)
It was said that there was 10% profit for selling a K.G of mixture for 68.20 rs. But we generally know for any good of C.P 100 rs, S.P of that good becomes 110 rs in case of 10% profit. Now, S.P - C.P. 110 - 100 => (10068.20)/110 = 62. 68. 20 - ? Now, by using the equation. (60(x)+65(y))/x+y = 62. On substituting values from options we get x=3 y=2, ratio becomes 3:2.

Nitin said: (Nov 4, 2016)
I think the ratio should be 2:3 not 3:2. Correct me if I am wrong.

Nitesh said: (Jan 21, 2017)
There will be profit, hence less price object will be in more than other. Hence, 3 : 2 only one option.

Sam said: (Jul 16, 2017)
I can't get it. Please explain.

Shubham Kumar said: (Mar 6, 2018)
Please explain the 2nd line ratio.

Ashutosh said: (May 3, 2018)
Anyone help me how to come 110?

Cosul said: (May 29, 2018)
Easy method applicable for all these kinds of problems. (quantity 1price 1+quantity 2price 2)/quantity 1+quantity 2 = mean quantity. %gain over CP =SP - CP. Hence,10% * CP =SP - CP. Upon solving you will get CP=100/110 * SP. = 62 rs (60(x)+65(y))/x+y = 62. If you solve it you get x/y =3/2.

Jyotsana said: (Apr 11, 2019)
I think the ratio should be 2:3.

Zahir said: (Sep 25, 2019)
We know, Gain%= (SP-CP)/CP. Let, the amount of tea Rs.65 is x kg. And the amount of tea Rs.60 is y kg. Now, CP= 60x+65y. SP= 68.20(x+y), So according to the gain% formula. [{68.20(x+y)-(60x+65y)}/(60x+65y)]=10/100, => x/y=3/2.