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 2 of 5.
Naveen kumar said:
9 years ago
Because they asked to find about 2nd one only.observe the allegation rule the no below 18% is 6. So that must be calculated .the ratio is 4:6 it means that (6/10) * 1000 = 600.
We get the answer. Hope you got it.
We get the answer. Hope you got it.
Abhi M said:
8 years ago
Hey Guys,
I have a question.
When the quantities are all expressed in percentages, can we take the values as it is? Without having to find out the Cost Prices or Selling Prices?
I have a question.
When the quantities are all expressed in percentages, can we take the values as it is? Without having to find out the Cost Prices or Selling Prices?
Chinki said:
8 years ago
Why 2/3 is not multiplied by 1000?
Asha said:
8 years ago
@Chinki
Because they have asked only about the quantity which is sold for 18% profit
if they asked to fine out the quantity which is sold for 8% profit you can multiply 2/5 (bcs 2/(3+2)) with 1000.
=(2/5) * 1000 => 400kg.
Because they have asked only about the quantity which is sold for 18% profit
if they asked to fine out the quantity which is sold for 8% profit you can multiply 2/5 (bcs 2/(3+2)) with 1000.
=(2/5) * 1000 => 400kg.
Aditya said:
8 years ago
A businessman sells some sugar in total sugar of 50 kg on 8% profit and remaining sugar on 18% profit. If the average profit is 14%. Find the amount of sugar which was sold on 18% profit.
Can anyone solve this?
Can anyone solve this?
Lucky said:
8 years ago
Thank you all.
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.
Shree said:
8 years ago
Thank you all for explaining the solution.
Chanukya said:
7 years ago
Thank you helped me.
Yogesha said:
7 years ago
How to calculate 1st ratio and 2nd ratio? Please tell me.
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers