Aptitude - Alligation or Mixture - Discussion
Discussion Forum : Alligation or Mixture - General Questions (Q.No. 15)
15.
A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is:
Answer: Option
Explanation:
By the rule of alligation, we have:
| Profit on 1st part Profit on 2nd part | ||
| 8% | Mean Profit 14% | 18% |
| 4 | 6 | |
Ration of 1st and 2nd parts = 4 : 6 = 2 : 3
 Quantity of 2nd kind = |
 |
3 | x 1000 |  kg |
= 600 kg. |
| 5 |
Discussion:
45 comments Page 5 of 5.
Nafiul said:
6 years ago
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.
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.
Andy said:
6 years ago
8x + 18(1000-x)/x+1000-x =14.
8x+18000-18x = 14000,
Solving x you get 400,
1000 - 400 = 600.
8x+18000-18x = 14000,
Solving x you get 400,
1000 - 400 = 600.
(2)
Gokul Ramakrishnan said:
5 years ago
Thank you it helped me a lot.
MANISH said:
4 years ago
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.
18-14 = 4.
Ratio of 1st = 2:3.
Now;
2+3 = 5,
5 units = 1000,
1 units = 200, then
3 units = 3*200 = 600.
(5)
Sylvester OgboluOtutu said:
2 months ago
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.
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.
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