Aptitude - Alligation or Mixture - Discussion

This is same as last problem. Here goes:
Selling price is 9.24 and profit is 10% so:
Cost price + Profit = Selling Price
Let cost price be equal to x:
x + 0.1x = 9.24
1.1x = 9.24
x = 924/11 which is 8.4

Then you do alligation which is shown in the explanation to bring the ratio of Rs. 9 sugar to Rs. 7 sugar down to 7:3

So Amount of Rs. 9 sugar (lets call it A) is related to amount of Rs. 7 sugar by the following formula:
A/27 = 7/3 (since we found out the ratio they are in)
Now solve for A by cross multiplying:
3A = 27 x 7
A = (27 x 7)/3 [27/3 reduces down to 9) = 9 x 7 = 63kg

Since, at the profit of 10%,

Selling price tk 110 than cost price tk 100.

Selling price tk 1 than cost price tk 100/110.

Selling price tk 9. 24 than cost price tk 100*9.24/110 = 8.40.

Let, sugar will be mixed x kg.

X kg sugar at tk 9 than cost price will be tk 9x.

27 kg sugar at tk 7 than cost price will be tk 27*7 = 189.

Total cost price = (9x+189).

According to the question,

(9x + 189)/(x+27) = 8.40.

=> 9x + 189 = 8.40x+ 226.8.

=>. 60x = 37.80.

=> x = 63 kg.

Observe the allegation method which is given as solution. They are mixed in the ratio 1.40:0.60 =14:60. This ratio always remains constant in allegation. They have already given 27kg for sugar costing 7rs/- per kg. The question asked is how many (?) kgs of sugar costing 9rs/- per kg should be mixed. So equate the ratio of weights.

I have an easy and understandable way I hope for you guys,

Let x be the quantity we are looking for, and qty A be 7/kg while qty B is 9/kg.

Based on unit equivalency;

[(qty A*price of A)+(qty B*price of B)]profit = total amount*9.24.

Thus, (27*7 + x*9)*1.1 = (27 + x)*9.24.

Solve for x, and you will get x = 63.

@All. Here's my explanation.
Let x kg of 9 Rs. sugar.
Total cost before gain = (9*x + 27*7),
and after gain = (9*x + 27*7) * 1.1 where (10% gain).

This total cost should be equal to 9.24 * (27+x)
By solving, 9.24 * (27+x) = (9*x + 27*7) * 1.1
x = 63.

Unit C.P : Qty : Total Amount

Item 1. : 9 : x : 9x

Item 2. : 7 : 27 : 189

Mixture : 8.4 : x+27 : 8.4(x+27)


---> 9x+189 = 8.4x + 226.8.
---> 0.6 x = 37.8.
---> x = 63.

From where does this value 1.40 & 0.60 came from?

And there after ratio?

Please help me out.

Anyone having much better and simpler ideas than this one can openly suggest and guide.

Thank you. Hoping for an early reply.

Solve in another method: Amount of 1st kind 'x'and its cost Rs.9/kg and amount of 2nd kind is 27kg and its cost is 7/kg.
c.p of mixture=(9x+(27*7))
s.p of mixture=9.24*(27+x)
Profit=(s.p-c.p)/c.p=10/100
Then we get x value.

Here, gain of 10% by selling the mixture at 9.24 per kg. So, the cost price per kg in mixture, x+ 10% of x= 9.24,
so, x= 8.4.

Let, x kg of sugar costing 9 per kg mixed in the mixture.
So, 9*x+7*27 = 8.4(x+27),
so, x= 63.

Let the the quantity of 9 per kg sugar be X.

CP = (X*9)+(27*7) = 9X+189
SP = 9.24*(X+27)

GAIN%=(PROFIT/CP)*100
ie ((SP-CP)/CP)*100 = 10

SUBSTITUTE THE VALUES IN ABOVE EQN AND SOLVE FOR X

i.e. X = 63.