Aptitude - Alligation or Mixture - Discussion

The quantity sold at 18 per cent profit is 600 kg.

Representations:

Let the quantity sold at 8% profit = x, and the quantity sold at 18% profit = y.

0.08 ● x = 0.08x.
0.18 ● y = 0.18y.

The combined profit is 14% = 0.14 ● (x + y) = 0.14(x + y).

It is given that:

x + y = 1000, and;
0.08x + 0.18y = 0.14(x + y)
0.08x + 0.18y = 0.14x + 0.14y
0.18y - 0.14y = 0.14x - 0.08x
0.04y = 0.06x
4y = 6x
4y/4x = 6x/4x
y/x = 6/4
y/x = 3/2.
Ratio of x : y = 2 : 3
1000 ÷ 5 = 200.
x => 2 × 200 = 400 kg.
y => 3 × 200 = 600 kg.

Checking:
400kg × 0.08 = 32
600kg × 0.18 = 108
1000kg = 32 + 108 = 140
140/1000 = 0.14 => 14 per cent (Checked)

Alternatively;

Given;
x + y = 1000; and,
0.08x + 0.18y = 0.14(x + y)
0.08x + 0.18y = 0.14x + 0.14y

From;
x + y = 1000
x = 1000 - y
Substitute 1000 - y for x;
0.08(1000 - y) + 0.18y = 0.14(1000 - y) + 0.14y
80 - 0.08y + 0.18y = 140 - 0.14y + 0.14y
80 + 0.1y = 140.
0.1y = 140 - 80,
0.1y = 60,
y = 60 ÷ 0.1,
y = 600.
The quantity sold at 18 per cent profit is 600kg.

14-8 = 6.
18-14 = 4.

Ratio of 1st = 2:3.

Now;
2+3 = 5,
5 units = 1000,
1 units = 200, then
3 units = 3*200 = 600.

Thank you it helped me a lot.

8x + 18(1000-x)/x+1000-x =14.
8x+18000-18x = 14000,
Solving x you get 400,
1000 - 400 = 600.

Ql=Quality of Lower.
Qh=Quality of Higher(Let x).
Pl=Profit of Lower.
Ph=Profit of Higher.

Ql/Qh=(Ph - M)/(M - Pl).
(1000-x)/x=(18-14)/(14-8).
(1000-x)/x=4/6.
(1000-x)/x=2/3.
2x=3000-3x.
5x=3000.
x=600.

How to calculate 1st nd 2nd ratio?

How to calculate 1st ratio and 2nd ratio? Please tell me.

Thank you helped me.

Let x part is sell with 8% profit
And the rest 1000-x with 18%
And total profit is 14%.

Then we can write;

(X * 8) (1000-x)*18 (1000 * 14)
---------------- + ----------- = ------------------
100 100 100

Here all 100 in the denominator is cancel out;
And we get,
8x + 1000*18 - 18x = 1000*14
-10x = 14000 - 18000
-10x = -4000
X = 400.

The quantity sold at 18% profit is:

1000 - x = 1000 - 400 = 600 Ans.

I HOPE IT WILL HELP TO MAKE WITH BASIC WITHOUT ALLIGATION METHOD.

THANK YOU.

Clear explanations. Thanks for your great help.